When Representative Kevin McCarthy was short the votes he needed to become speaker in January, he didn’t browbeat his far-right Republican detractors or threaten retribution. Instead, he granted them major concessions, subjecting himself to a long, humiliating slog to win them over.

Mr. McCarthy is now facing a near-certain government shutdown and a possible move by the same faction to oust him from his post if he moves to head off the crisis. And he is turning to the same people-pleasing script, seeking to mollify a faction of his conference he privately scorns.

He has once again caved to the demands of far-right lawmakers, opening an impeachment inquiry into President Biden and then agreeing to slash government spending to levels they clamored for. When that was not enough, Mr. McCarthy pushed aside a stopgap spending bill to avert a government shutdown. Instead, he bowed to the right flank’s insistence on first bringing up a series of individual yearlong spending bills loaded up with arch-conservative policy dictates — even though none had a chance of enactment.

Democrats have criticized him as the weakest speaker in history. Hard-right members continue to demand more. But members of Mr. McCarthy’s inner circle — a coterie of mostly traditional Republicans who are deeply conservative but share little in common with the hard right — argue that the speaker’s malleability is actually his strength. They say it is the only way to deal with what they regard as a nearly ungovernable majority.

“He is in the driver’s seat, but he’s also willing to ask members in the car to help him navigate,” said Representative Dusty Johnson, a South Dakota Republican and McCarthy loyalist. “That is not — with all due respect to other speakers — they have mostly been interested in taking everyone in the car where they wanted to go.”

Yet with a four-vote voting margin and a far right that appears bent on forcing a shutdown, Mr. McCarthy’s car is spinning out of his control.

In recent days, he and his confidants have weighed bringing up a temporary spending bill they know lacks the Republican support necessary to pass simply to show the public that they tried to keep the government open — a step that would likely have been deemed unthinkable by many of his predecessors.

“Increasingly, members have been going to McCarthy to say we have to vote on it anyway,” Mr. Johnson said. “We need to show a good-faith effort to not shut down the government.”

The group of allies advising Mr. McCarthy, a California Republican, as he navigates another difficult chapter in his speakership also includes Representative Garret Graves of Louisiana, who has no official leadership role but has become the speaker’s crisis consigliere; Representative Patrick T. McHenry of North Carolina, his longtime sounding board; and Representative French Hill of Arkansas, an old-school Republican who looks and sounds like he comes from a different political party than the rebels who are tying the House in knots.

As chairman of the Main Street Caucus, Mr. Johnson has been in constant contact with Mr. McCarthy since he took on the lead role in trying to work with members of the hard-right House Freedom Caucus to find a stopgap funding deal that could pass.

Representative Jim Jordan of Ohio, a foe-turned-friend who has become a bellwether for what conservatives can stomach, has been offering advice, too. For months, he has been telling Mr. McCarthy that he needs to get the funding level of any stopgap bill as low as possible and then ask for one big policy concession from the Democrats that he can win: tighter restrictions on the border. But even that has so far proved to be a nonstarter with the rebels.

As days go by and House Republicans squander any leverage they might have to influence the Democrat-controlled Senate, choosing the least bad option has become the sad refrain of Mr. McCarthy’s closest allies.

That has left him celebrating any progress — however tiny — he can muster, such as the passage this week of a routine procedural measure that allowed several spending bills to go to the House floor for debate. Under previous speakers, winning adoption of such a measure, known as a rule, was a foregone conclusion; Mr. McCarthy has lost three in the past eight months.

“Many of you asked the question many times, could you pass the rule,” Mr. McCarthy said at a late-night news conference at the Capitol that served as a feeble victory lap for a race that was far from finished. “Now I just want to let you know that the rule has passed.”

Former Speaker Newt Gingrich, the Georgia Republican who led the G.O.P. revolution of 1994 and tried to wield a 21-day government shutdown as a political weapon against former President Bill Clinton, said Mr. McCarthy faces a far more difficult predicament.

“I could never manage this kind of majority,” Mr. Gingrich said. “It takes patience, it takes focusing on individuals, it takes resilience. Kevin has what will be a continuing problem, and that is his margin is just too small.”

But Mr. McCarthy’s problem is not only the punishing math. Some of his colleagues say he has made so many promises to members that they simply do not trust him.

Mr. McHenry, however, argued that the speaker has made progress in uniting his conference since January, when a group of 20 members branded themselves as “Never Kevins” and had to be slowly won over with concessions.

“The speaker has proven himself to those that were strongly in his favor — the 200 that were strongly in his favor in the opening week,” Mr. McHenry said between meetings at the Capitol on Friday last week, dressed down in jeans and a T-shirt after Mr. McCarthy had sent lawmakers home for the weekend, scrapping plans for a weekend session because there was no agreement on what to do.

He noted that some of the onetime G.O.P. holdouts, like Representatives Chip Roy of Texas and Byron Donalds of Florida, were now working with Mr. McCarthy rather than against him.

“They’re inside trying to solve problems instead of sitting across from us,” Mr. McHenry said. “The players are similar — actually the same — but where people are sitting is a little bit more toward our favor in being able to function and originate policy.”

The players may have shifted in their seats around the table, but as Congress careened toward a shutdown, it was still the far-right members of the conference who appeared to be dictating both policy and procedure, with Mr. McCarthy merely reacting to their desires.

So rather than quickly putting a spending patch to a vote, Mr. McCarthy spent the precious final days before a shutdown deadline at midnight on Saturday passing proposals from the hard right, such as slashing the salary of Defense Secretary Lloyd J. Austin III to $1 — a measure proposed by Representative Marjorie Taylor Greene, Republican of Georgia — canceling Mr. Biden’s executive orders to counter climate change and doing away with a Pentagon office of diversity, equity and inclusion.

Still, Mr. McHenry said, having been through his tumultuous race for the speakership and a high-stakes negotiation with Mr. Biden to head off a federal debt default, Mr. McCarthy was up to facing the current crisis, which he described as “more complicated but less existential” than either of those.

“We’ve been through a government shutdown before,” he said. “This has a different feel.”