Hard-right Republicans pressed their mutiny against Speaker Kevin McCarthy into a second day on Wednesday, keeping control of the House floor in a raw display of their power that raised questions about whether the speaker could continue to govern his slim and fractious majority.

Mr. McCarthy, who enraged ultraconservative Republicans by striking a compromise with President Biden to suspend the debt limit, has yet to face a bid to depose him, as some hard-right members have threatened. But the rebellion has left him, at least for now, as speaker in name only, deprived of a governing majority.

“House Leadership couldn’t Hold the Line,” Representative Matt Gaetz, Republican of Florida and a leader of the rebellion, tweeted on Wednesday. “Now we Hold the Floor.”

After being forced for the second day in a row to cancel votes as they haggled privately with members of the House Freedom Caucus to get them to relent, leaders told Republican lawmakers on Wednesday evening that they were scrapping votes for the remainder of the week. In a remarkable act of intraparty aggression, about a dozen rebels ground the chamber to a halt on Tuesday by siding with Democrats to defeat a procedural measure needed to allow legislation to move forward, and business cannot resume until they back down and vote with their own party.

It underscored the severe consequences Mr. McCarthy is facing for muscling through a debt ceiling agreement with the White House that contained only a fraction of the spending cuts Republicans had demanded. The episode has reignited divisions within Mr. McCarthy’s own leadership team, with the speaker suggesting his No. 2 was in part to blame for the dysfunction. And it was a blunt reminder of the challenge Mr. McCarthy will face in holding together his conference to pass crucial spending bills this year, which will be required to avert a government shutdown this fall and punishing across-the-board spending cuts in early 2025.

The paralysis that has gripped the House this week — an exceedingly rare instance of a faction of the majority holding its own party hostage — recalled Mr. McCarthy’s weeklong, 15-round slog to win his post, which required him to win over many of the same hard-right lawmakers instigating the current drama.

On Wednesday night, Mr. McCarthy conceded that there was “a little chaos going on,” though he insisted that he would get the party agenda back on track.

“We’ve been through this before; you know we’re in a small majority,” Mr. McCarthy told reporters earlier in the day. “I don’t take this job because it’s easy. We’ll work through this, and we’ll even be stronger.”

But he also appeared to blame the impasse at least in part on Representative Steve Scalise of Louisiana, the majority leader, saying that he had caused a misunderstanding that paved the way for the spontaneous hijacking of the House floor on Tuesday.

“The majority leader runs the floor,” Mr. McCarthy said.

The temper tantrum from the right had little immediate impact other than to deprive Republicans of the chance to pass a messaging bill that was all but certain to die in the Senate. The legislation that the rebels blocked is aimed at guarding against government restrictions on gas stoves and other federal regulations.

But ultraconservative Republicans said much more was at stake, arguing that Mr. McCarthy had betrayed promises he made to them during his fight for the speakership and now had to be forced into honoring them.

“There was an agreement in January and it was violated in the debt ceiling bill,” said Representative Ken Buck, Republican of Colorado. He said the conversations with Mr. McCarthy on Wednesday were to discuss “how to restore some of that agreement.”

In the meantime, some rank-and-file Republicans lamented the spectacle — “political incontinence,” Representative Steve Womack of Arkansas called it — and predicted a major backlash against their party in 2024 if they did not get themselves in order soon.

“We are wetting ourselves and we can’t do anything about it,” Mr. Womack said. “This is insane. This is not the way a governing majority is expected to behave, and frankly I think there’ll be a political cost to it.”

In some sense, the drama was a reset to how House Republicans have long functioned, with a speaker constantly threatened by a small group of hard-right bomb throwers who make his job impossible unless he bows to their demands. Former Speaker John A. Boehner of Ohio resigned from Congress in 2015 under pressure from House conservatives who repeatedly threatened to move to topple him.

But Mr. McCarthy has been set on not replicating those mistakes, trying to defang his biggest detractors by rewarding them with committee chairmanships and powerful positions on the Rules Committee. That approach appeared to have worked, until Mr. McCarthy, knowing that the right wing would not provide the votes to pass a debt limit bill, worked with Democrats to push through the legislation just days before a default.

“We’re back to the normal state of affairs where the speaker has to worry about this group — and that’s how it’s been for a decade,” said Brendan Buck, who was a top adviser to Speaker Paul D. Ryan of Wisconsin and Mr. Boehner. “These guys want to be relevant more than anything else. They find a way to reassert themselves into the conversation.”

Former speakers have had to suffer the embarrassment of pulling bills from the floor because they did not have the votes to pass their legislation. But it had been almost 21 years since a procedural measure had been defeated on the House floor, as occurred on Tuesday.

Mr. McCarthy had privately leaned on Republicans not to resort to such a move. In the weekly party conference meeting on Tuesday morning, he said lawmakers were always free to vote against a bill they did not like, but should never take actions that turn the floor over to the minority, such as voting against a procedural motion, as many of them had done in a bid to block the debt ceiling bill from being considered, according to two people familiar with the meeting.

Hours later, about a dozen Republicans did just that, voting with Democrats against allowing the regulatory bills to come up.

Representative Tom Emmer of Minnesota, the majority whip, called the episode a minor setback after several months of a well-functioning House, and blamed it on “an accumulation of frustration that’s been building since January.”

“Don’t expect that it’s always going to be like this,” he said. “Every team will encounter adversity at some point. That’s literally what we’re going through.”

It was not clear exactly what the members of the Freedom Caucus were demanding in exchange for surrendering control of the floor.

“They don’t know what to ask for,” Mr. McCarthy said on Wednesday night. “There’s numerous different things they’re frustrated about.”

And Mr. Gaetz made it clear that demands were secondary to forcing Mr. McCarthy to make a defining decision — whether he wanted to pass bipartisan bills with Democrats or have the support of the far right.

“We’re going to force him into a monogamous relationship with one or the other,” he said in an interview on “War Room,” the podcast hosted by Stephen K. Bannon. “What we’re not going to do is hang out with him for five months and then watch him go jump in the back seat with Hakeem Jeffries.”

Karoun Demirjian contributed reporting.