For weeks, House Speaker John A. Boehner (R-Ohio) tried to be the kind of speaker he wanted to be, with dreams of negotiating a big budget deal with President Obama. On Friday, he became the kind of speaker he had to be, yielding to rebellious tea party conservatives and altering his bill to raise the debt ceiling to avoid a humiliating defeat.

But that was hardly a resolution of the crisis. It was a victory — on his fourth try — that underscored the gap between the parties, as the bill was immediately scuttled in the Senate.

On Saturday, the search for a real compromise began, with both sides vowing to try to pass something before Tuesday’s deadline. When a measure returns to the House, Boehner and his lieutenants will face perhaps their most severe test as they attempt to round up votes for a bill certain to be even less palatable to conservatives than the one approved Friday.

All this has created doubts about Boehner’s leadership. Will he emerge from this battle weakened, or, despite the setbacks he has endured, could he find himself strengthened within his party? Democrats and some in the media already have cast him as surely weakened, and there is speculation about his eventual hold on power depending on how the final chapter plays out.

Boehner has remained the upbeat, if emotional, warrior in these last days, evidenced by his comments at a meeting of Republicans on Friday morning and his fiery speech on the House floor Friday night. For now, Republicans have rallied around him publicly, or at least given him the benefit of the doubt.

“I think he’s gotten through this better than most people might initially believe,” said Rep. Tom Cole (R-Okla.). “I think Boehner is strong with the members. Even the members who didn’t vote with him respected the manner in which he operated.”

But as the week showed, respect isn’t enough. Rep. Jason Chaffetz (R-Utah) opposed both versions of the Boehner bill.

“I told the speaker: ‘I support you. I just don’t support your bill,’ ” Chaffetz said.

The debt-ceiling battle leaves the ultimate judgment on Boehner’s speakership — and the reputation of his leadership team — open. There is no question that leading the House today is more difficult than in some times past, given intense partisanship and a Republican conference that includes 87 new members, many of whom came to Washington with tea party backing and a determination not to play by accepted rules.

Republican leaders took advantage of that sentiment to win their majority in November. Did they underestimate the problems that could lead to as they tried to govern?

At the same time, it is unclear whether a stronger speaker, with a greater command of his sometimes-defiant membership, could have coaxed them to accept the kind of deal that was on the table with the president.

Aides to Boehner would respond only to written questions about the impact of the battle on the speaker’s reputation. Spokesman Michael Steel said that, almost no matter the outcome, the speaker and his party can take credit for changing the debate in Washington.

“Has it been messy at times?” he wrote. “Yes, but Republicans will achieve substantial cuts and reforms at the end of the process.”

Left to his own devices, Boehner clearly preferred to negotiate a comprehensive deal. This, after all, is a speaker who fell out of leadership in the 1990s in part because his colleagues thought he was too willing to deal with the Democrats.

But in the current House, he cannot always work his will, even with his own party.

“Even with a majority, the speaker can’t control the events in the House,” said Ross K. Baker, a political scientist at Rutgers. “I won’t say it’s unprecedented, but it’s certainly an event equivalent to the total eclipse of the sun.”

A senior Democratic aide who spoke on the condition of anonymity in order to talk freely about the speaker, said Nancy Pelosi (D-Calif.) faced a far more diverse caucus as speaker and managed to pass a host of difficult bills.

“These guys have a wildly homogenous caucus,” the aide said, “and they can’t pass a bill to cut spending. I don’t get it.”

And there is criticism even among some Republicans over the way the leadership handled the meltdown Thursday night.

Thursday’s events were revealing for what they say about both the leadership and the Republicans they are attempting to lead. One Republican legislator after another trooped into Boehner’s office so the speaker could make his appeals. House Majority Leader Eric Cantor (R-Va.) cornered them on the House floor. House Majority Whip Kevin McCarthy (R-Calif.) opened his offices to some of the rebels and served pizza. Lawmakers ate the pizza but didn’t change their minds.

A leadership aide said the fact that Boehner responded by redrawing his bill did not set a bad precedent. “The speaker has been clear that the majority is going to operate differently,” said Cantor spokesman Brad Dayspring. “It’s going to operate collectively.”

One of the holdouts at the McCarthy pizza party was freshman Rep. Mo Brooks (R-Ala.). He said he let out a whoop Friday morning when he heard that Boehner was making changes in his plan, including a requirement that Congress approve a balanced-budget amendment to the Constitution before a second increase in the debt ceiling could occur.

Had he and his fellow holdouts shown that the House was no longer governable under the normal terms?

“We’re the people’s house,” he said. “We’re not supposed to be governed.”

Boehner’s colleagues sympathized with his situation Thursday, even as they resisted. Rep. Raul R. Labrador (R-Idaho) said the speaker was making the best of a difficult situation. “He knew he could not come to [me] and say, ‘Hey, you’ll get a bridge in Idaho,’ ” Labrador said. “He’s trying to use gentle persuasion.”

Sen. Richard Burr (R-N.C.), one of Boehner’s closest friends, said Boehner’s relatively light touch is simply the way the speaker prefers to do business. “That’s not going to change,” he said.

Even if Boehner had tried to strong-arm the holdouts, he would have risked further embarrassment.

“You can even physically whip [the holdouts] and you’re not going to get these guys to believe that the world ends on August 2nd,” said Rep. Devin Nunes (R-Calif.).

Not even gentle persuasion could overcome higher powers Thursday. As Boehner was in his meetings, three freshman Republicans from South Carolina were in the House chapel nearby, in quiet discussion and in prayer. Reps. Mick Mulvaney, Tim Scott and Jeff Duncan wanted a stronger provision to guarantee a balanced-budget amendment and knew they would be lobbied furiously in the hours to come.

At one point, Duncan said, Mulvaney picked up a Bible and read a verse from Proverbs 22: “The rich ruleth over the poor, and the borrower is servant to the lender.”

“It’s telling me to really be bold, to really fight for structural changes,” Duncan said.

“Mulvaney snapped the Bible closed. And I said, ‘Guys, that’s all I need to see,’ ” Duncan said. “Tim said, ‘Yep.’ And we stood up and walked out.”

Boehner has faced challenges as well, or at least the perception of challenges, from his own leadership team. Cantor long has been seen as, if not a direct rival, an uncertain ally to the speaker in some of the battles.

It was Cantor, others say, who played the most direct role in helping to upend the initial round of negotiations between the speaker and the president. Over the past two weeks, however, Cantor has stood firmly with Boehner.

McCarthy’s whip operation has come in for criticism for its handling of the Boehner bill that was pulled from the floor. Veteran Republicans say the current whip operation is far less effective than those in previous Congresses.

Freshman Rep. Todd Rokita (R-Ind.), a reluctant supporter of the original Boehner plan, said he appreciated the speaker’s willingness to give in without punishing those who held out. But he pointed to Boehner’s next problem, which will be corralling a bipartisan majority for whatever compromise that may emerge from the weekend. “There’s been an amazing test of his leadership already,” Rokita said, “and his test may not be over.”

Staff writers Rosalind S. Helderman, Paul Kane, Lori Montgomery and Felicia Sonmez contributed to this report.