McCarthy’s journey to the speakership foreshadowed a fractious House.

That there isn’t an obvious answer to the question was part of Mr. McCarthy’s ability to win the bruising battle for the job in the first place — he never let a serious alternative emerge.

Nine months later, there still isn’t a clear candidate in waiting.

“I think there’s plenty of people who can step up and do the job,” Representative Tim Burchett of Tennessee, one of the rebels bent on pushing Mr. McCarthy out, said Tuesday morning, but he said he did not know who he had in mind for the job instead.

Representative Eli Crane of Arizona, another one of the hard-line holdouts against Mr. McCarthy, said he wasn’t there yet in terms of supporting someone else.

“I don’t like to get the cart before the horse,” he said. “For me, right now, this is just about representing my voters and holding the speaker accountable for deals made and deals broken."

Some names were starting to be bandied about, even as all of the potential successors vowed that they were not looking to replace Mr. McCarthy, who they said they still supported.

Representative Matt Gaetz, Republican of Florida, on Monday night said he was open to supporting Representative Steve Scalise of Louisiana, the current No. 2 House Republican and a longtime McCarthy rival who is undergoing chemotherapy treatment for blood cancer.

“I am not going to pass over Steve Scalise just because he has blood cancer,” Mr. Gaetz told a horde of reporters as he left the Capitol on Monday night.

Representative Tom Emmer of Minnesota, the No. 3 Republican in the House who serves as the majority whip, has also been mentioned by some of his colleagues as a viable option. Mr. Emmer, who has hosted many late night sessions in his office with various factions of the Republican conference, trying to help the group find common ground, has gained the trust of the far-right members. But they don’t view him as a particularly strong leader.

“He’s a good sounding board. He’s got some nice conference rooms. He doesn’t lie to us,” Mr. Gaetz said of Mr. Emmer in an earlier interview. “We know he can’t make anything happen.”

Another logical person to turn to would be Representative Patrick McHenry, the longtime North Carolina congressman who is close with Mr. McCarthy and has previously served in leadership. But Mr. McHenry would most likely resist any attempt to draft him into the role. He chose not to run for a leadership role last year, opting instead to lead the powerful financial services committee.

In a scramble, Representative Elise Stefanik, the top woman in leadership whose role means she works closely with all members of the conference, could emerge as another potential alternative. Serving as conference chair and overseeing messaging for all House Republicans, she is widely seen as someone with big political ambitions outside of the House — like potentially serving in a future Trump administration.

Representative Tom Cole of Oklahoma, one of the longest serving Republicans in the House who leads the Rules Committee, is also respected by both Republicans and Democrats alike.

Mr. McCarthy clawed his way to victory by cutting a deal that won over a sizable contingent of ultraconservative lawmakers on the 12th and 13th votes earlier in the day, then wearing down the remaining holdouts in a tense session that dragged on past midnight. He ultimately won with a bare majority after a spectacle of arm-twisting and rancor on the House floor.

The protracted process foreshadowed how difficult it would be for him to govern with an exceedingly narrow majority and an unruly hard-right faction bent on slashing spending and disrupting business in Washington. The speakership struggle that crippled the House before it had even opened its session suggested that basic tasks such as passing government funding bills or financing the federal debt would prompt epic struggles over the next two years.

Yet Mr. McCarthy, who was willing to endure vote after humiliating vote and give in to an escalating list of demands from his opponents to secure the post, denied that the process foretold any dysfunction.

“This is the great part,” he told reporters. “Because it took this long, now we learned how to govern.”

Despite the divisions on display, Mr. McCarthy also emphasized the theme of unity in a speech after taking the speaker’s gavel, pledging open debate and an open door to both Republicans and Democrats. “You can see what happens in the people’s House,” he said.

The floor fight dragged on for the better part of a week, the longest since 1859, and paralyzed the House, with lawmakers stripped of their security clearances because they could not be sworn in as official members of Congress until a speaker was chosen.

Among the concessions Mr. McCarthy made to the ultraconservative lawmakers was allowing a single lawmaker to force a snap vote to oust the speaker at any time.

In January, 20 Republicans nearly derailed Mr. McCarthy’s ambitions to become speaker by voting against him multiple times. Eleven of them were among those who held out against his stopgap funding measure on Friday.

Mr. McCarthy’s five-day, 15-vote floor fight for speaker foreshadowed how hard it would be for him to corral Republican lawmakers to unify behind basic tasks like passing funding bills or raising the federal debt limit.

The minority leader, Representative Hakeem Jeffries, Democrat of New York, set the tone for the meeting by playing a video clip of an appearance Mr. McCarthy made on television on Sunday — the morning after Democrats helped him push through legislation to avert a government shutdown — in which he blamed them for trying to prompt a shutdown.

He waited until after many members had spoken to issue his marching orders to the caucus: that they should vote against any procedural motion brought to the House floor that would delay the removal of Mr. McCarthy.

Democrats said they had plenty of reasons to comply.

“I think he’s likely the most unprincipled person to ever be speaker of the House,” said Representative Abigail Spanberger, a centrist from Virginia who is considering a run for governor. “He’s disdainful, he lies about us, he lies about the process of governance. It’s not even a question of whether or not we should take any particular action.”

Democrats, for the most part, view Mr. McCarthy as a lackey for former President Donald J. Trump, and someone who has opened up a groundless impeachment inquiry into President Biden in order to appease the far-right members. They don’t trust him and regard him as someone who has made so many different promises to so many different people that his word is meaningless.

“They need to work this out,” Representative Rosa DeLauro of Connecticut said as she left the Democrats’ meeting. “This is not for us to get involved.”

Because of Republicans’ tiny majority and the size of the right-wing band of rebels pushing to remove Mr. McCarthy, he would most likely need at least some Democrats to support him or refrain from voting to survive.

Representative Mark Takano, a progressive from California, said that not one member in the room rose to make the case for voting “present” on the matter, which would lower the threshold for Mr. McCarthy to win a majority and stay in his post.

Instead, even the most politically vulnerable Democrats from swing districts have spoken out against him.

“If Kevin McCarthy hasn’t bothered to ask me or other Democrats for support, then why would we be putting much time into talking about this?” Representative Jared Golden of Maine, the co-chairman of the conservative Blue Dogs Caucus, said on Monday.

Representative Marie Gluesenkamp Perez of Washington, who also faces a tough re-election fight in a conservative district that Mr. Trump carried in two consecutive presidential elections, wrote on X, formerly Twitter, that “so far Kevin McCarthy is a lot more interested in appeasing guys like Joe Kent than talking with independent voices like me,” referring to the Republican she beat last year. Mr. Kent denied the legitimacy of the 2020 presidential election and supported defendants charged in connection with the attack on the Capitol on Jan. 6, 2021. She posted a picture of Mr. McCarthy and Mr. Kent posing together and smiling.

Here’s what happens next.

McCarthy can’t avoid a vote.

The resolution declaring the speakership vacant is privileged, meaning it takes priority in the House’s legislative agenda and requires action within two days.

The House of Representatives convenes at 10 a.m. on Tuesday, and legislative business begins at noon, the earliest that the motion could be acted upon.

Mr. McCarthy cannot avoid some sort of vote on the question, though he has some options for trying to divert or at least delay the vote.

McCarthy can try to kill the resolution.

The easiest and most likely course of action for the speaker is to move to table Mr. Gaetz’s resolution, effectively killing it. That, too, requires a majority vote of the House. Should he be successful, the fight would be over and Mr. McCarthy would keep his job.

Should his motion to table be defeated, the House would move to a vote on the resolution to remove him.

Another possible but less likely move for Mr. McCarthy would be to move to refer the question to a congressional committee, effectively punting it to a group made up of his allies. He engineered a similar move in June that sidestepped an attempt to quickly impeach President Biden. That would also require a majority vote.

McCarthy is all but certain to need Democrats to survive.

The Republicans’ slim majority and the size of the far-right group pressing to remove him means that Mr. McCarthy has little chance of winning any one of the possible votes and keeping his job without at least some help from Democrats.

As of Monday, House Democrats had not signaled their intentions, and Mr. McCarthy said Tuesday morning that he would not offer them anything in exchange for their support.

It is extremely rare for members of the minority to vote for the opposing party’s candidate for speaker. Democrats voted in unison for their leader, Hakeem Jeffries of New York, in each of the 15 rounds of the speakership fight in January. And Mr. McCarthy’s efforts to appease far-right members within his party since then, including launching an impeachment inquiry into Mr. Biden last month, have further frustrated Democrats.

If some Democrats did decide to help save Mr. McCarthy, the simplest way would be for them to vote to oppose Mr. Gaetz’s ouster resolution, and vote to table it. They could also help the speaker in a more passive way, either by voting “present” — neither yes or no — or skipping the vote entirely. Both moves would lower the threshold of votes he needs to survive.

If the ouster fails, McCarthy could face another one.

Mr. Gaetz has said that he might keep trying to remove Mr. McCarthy over and over again — even daily. There is nothing in the House rules to prevent this. His move on Monday was only the third time in the 234-year history of the House that a speaker has faced a motion to vacate.

Most recently, in 2015, Representative Mark Meadows of North Carolina filed a motion against Speaker John A. Boehner, who resigned from Congress before the House voted.

If McCarthy is removed, the House would be paralyzed.

A vacancy in the speaker’s chair would essentially paralyze the House until a successor is chosen, according to multiple procedural experts. An interim speaker would be chosen from a list prepared by Mr. McCarthy and his staff at the beginning of the year, but staff intimately familiar with House rules say the role of that person would be to oversee a speaker election and little more.

Carl Hulse contributed reporting.

The move came just days after Mr. McCarthy opted to avert a government shutdown the only way he could — by relying on Democratic votes to push through a stopgap spending bill over the objections of an unmovable bloc of hard-liners in his own party, including Mr. Gaetz.

It was a brief but tense interruption of the day-to-day proceedings of the House. Mr. McCarthy was not present on the House floor when Mr. Gaetz made his motion, but scores of Democrats crowded in the aisles to watch the spectacle. The House adjourned shortly afterward, but under the chamber’s rules, Mr. McCarthy and his leadership team will need to address it within two legislative days.

“It is becoming increasingly clear who the speaker of the House already works for, and it’s not the Republican conference,” Mr. Gaetz said earlier Monday, making the case for Mr. McCarthy’s ouster. He added that the speaker had allowed President Biden to take his “lunch money in every negotiation.”

Mr. Gaetz cited Mr. McCarthy’s dependence on Democrats to pass the funding bill — which was necessary to avert a shutdown because Mr. Gaetz and 20 of his colleagues opposed a temporary funding bill. And he accused Mr. McCarthy of lying to his Republican members during spending negotiations and making a “secret deal” with Democrats about funding for Ukraine, which he and dozens of other conservatives have opposed.

The move is a significant escalation of the long-simmering power struggle between Mr. McCarthy and a clutch of conservative hard-liners in his party. They have dangled the threat of dethroning the speaker since he was elected, after they subjected him to a painful round of 15 votes.

Mr. McCarthy, a chronic optimist who has shown a remarkable willingness to weather political pain to maintain his grip on the speaker’s gavel, appeared undaunted. Minutes after Mr. Gaetz filed the resolution, he wrote on social media, “Bring it on.”

“I think it’s disruptive to the country, and my focus is only on getting our work done,” Mr. McCarthy said earlier Monday. “I want to win the vote so I can finish the job for the American people. There are certain people who have done this since the day we came in.”

Mr. Gaetz’s animus toward Mr. McCarthy extends far beyond the most recent funding skirmish. He emerged as Mr. McCarthy’s chief tormentor during the speaker’s fight in January, when he suggested on the House floor that the California Republican had “sold shares of himself for more than a decade,” and never quite stopped.

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It was to appease Mr. Gaetz and the 19 other Republicans who opposed his speakership that Mr. McCarthy agreed to change the rules of the House to allow any one lawmaker to call a snap vote for his ouster.

After Mr. McCarthy struck a bipartisan deal with Mr. Biden in the spring to suspend the debt ceiling, there were rumblings among the far right about moving forward on a motion to vacate. They settled for shutting down the House floor instead.

It was unclear how many Republicans planned to join Mr. Gaetz in his attempt to dethrone Mr. McCarthy. Some archconservatives who have been critical of the speaker have said in recent days that they would not support removing him now.

But Mr. Gaetz told reporters at the Capitol he had sufficient G.OP. backing to prevail — unless Democrats voted to save Mr. McCarthy.

“I have enough Republicans,” he said. Four other Republicans, Representatives Tim Burchett of Tennessee, Eli Crane and Andy Biggs of Arizona, and Bob Good of Virginia, have said they were inclined to support the motion. More have signaled openness to it.

It remained to be seen whether Democrats would help Mr. McCarthy maintain his post. If they were to vote against Mr. McCarthy — as is almost always the case when a speaker of the opposing party is being elected — Mr. Gaetz would need only a handful of Republicans to join the opposition to remove him, which requires a simple majority vote.

But Mr. McCarthy could hang onto his gavel if enough Democrats voted to support him, skipped the vote altogether or voted “present.” In that situation, Democrats who did not register a vote would lower the threshold for a majority and make it easier to defeat Mr. Gaetz’s motion.

Some Democrats representing moderate and conservative-leaning districts have indicated that they would be hard-pressed to punish Mr. McCarthy for working across the aisle to prevent a shutdown.

But others said they saw no reason to bail him out, pointing to the string of concessions Mr. McCarthy has made to appease his right flank. Those included opening an impeachment inquiry into Mr. Biden and reneging on spending levels negotiated with the president during the debt limit crisis.

In a statement, Representative Ilhan Omar, Democrat of Minnesota, savaged Mr. McCarthy for his opposition to abortion rights and measures to combat climate change. She called him “a weak speaker who has routinely put his self-interest over his constituents, the American people and the Constitution.”

Mr. McCarthy “has made it his mission to cover up a criminal conspiracy from Donald Trump, and is himself a threat to our democracy,” she said. “He literally voted to overturn the 2020 election results, overthrow the duly elected president and did nothing to discourage his members from doing the same.”

Mr. Gaetz’s antics have infuriated Mr. McCarthy’s allies, who view the Florida Republican’s campaign as a publicity stunt motivated by personal animus. As Mr. Gaetz waited to speak on the House floor on Monday, Representative Tom McClintock, Republican of California, rose and chastised him to his face without naming him. Mr. McClintock said he could not “conceive of a more counterproductive and self-destructive course” than to try to remove the speaker from one’s own party.

“I implore my Republican colleagues to look past their prejudices, their passions, their errors of opinion, their local interests and their selfish views,” Mr. McClintock said.

Even some Republicans who initially opposed Mr. McCarthy’s speakership indicated on Monday that they would not back Mr. Gaetz’s drive to dethrone him. Representative Chip Roy of Texas, an influential conservative, said on “The Sean Hannity Show” that he believed “the speaker deserves the ability to finish this year’s process.”

But he hinted that he would be open to getting rid of Mr. McCarthy if the speaker moved to approve aid to Ukraine without also securing the southern border.

“The gloves are off then,” Mr. Roy said.

There are a number of procedural sleights of hand that Mr. McCarthy and his allies could use to try to avoid an up-or-down vote on whether to keep him as speaker. He could hold a vote to table the resolution, which would effectively kill it, or refer it to a committee made up of his allies.

Still, Mr. Gaetz’s decision pushes the House into rarely tested waters.

Only two other speakers have faced motions to vacate: once in 1910, and more recently, in 2015, when Representative Mark Meadows, Republican of North Carolina, sought to oust Speaker John A. Boehner. The House never voted on the motion, but it contributed to Mr. Boehner’s decision to give up his gavel and resign from Congress.

Luke Broadwater and Karoun Demirjian contributed reporting.