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Democrats before seeking their consent.

"What we've seen in the past is the speaker goes, negotiates with the president, and just before we vote, he tells us what the deal is and attempts to persuade us to vote for it," said Representative John Fleming, Republican of Louisiana. "We're just not very happy with deals being baked, then we're asked to stay with the team and support the speaker."

Given those conflicting demands, Mr. Boehner must decide whether he wants to seal his role as an essential player in a grand plan to restructure the nation's fiscal condition, or continue the status quo of the very gridlock voters appear to detest.

"I don't want to box myself in, and I don't want to box anyone else in," Mr. Boehner told reporters on Friday.

Boehner aides say the situation is not as dire as the conflicts of the past two years, which nearly led to a government default on its debt and included a series of impasses that plunged Congress's approval rating to its lowest recorded level. Any deal with the president would probably lose 60 to 80 Republican votes, but the president would bring along enough Democrats to get it passed.

"When the president and I have been able to come to an agreement, there has been no problem getting it passed here in the House," Mr. Boehner assured reporters, alluding to the deal struck with Mr. Obama to extend payroll tax cuts, which took Democratic support.

On the conference call Wednesday, their ranks reduced by the election, House Republican leaders presented a united front, a departure from the backbiting of earlier showdowns, the leaders' aides admit. After acknowledging that the election had not gone the way any of them had hoped, Mr. Boehner made an ardent plea for unity, saying they could expect a good deal out of the coming negotiations only if they stuck together.

The handful of Republican backbenchers who spoke up agreed.

Before Mr. Boehner went in front of the cameras that afternoon with a carefully worded statement on the fiscal talks, aides say he checked in with another figure he will need on his side, Representative Paul D. Ryan of Wisconsin, the defeated vice- presidential nominee and the House Budget Committee chairman. He told Mr. Ryan what he was about to say and assured him he would be welcomed back as chairman, even though he needs a waiver to escape rules limiting chairmen's terms.

Mr. Ryan then went hunting and left Mr. Boehner to deliver his message.

But even his vague comments last week about his openness to new revenues to resolve the fiscal impasse -- and about a desire to work on some sort of immigration overhaul legislation, in a blunt acknowledgment of his party's weakness among Hispanic voters -- got immediate pushback from some members.

Some House Republicans have latched on to their own re-elections to claim a dual mandate.

"The message from this election for me seems to be, 'You guys keep going,"' said Representative James Lankford of Oklahoma. "The Senate was rewarded for inactivity, the House was rewarded for standing up for its principles and the president was rewarded for his. I was elected by my district to represent their values. I really don't approach this and say, 'Now I've got to cave to what the Senate or president want."'

Mr. Obama has continued to press his point that he campaigned clearly on a call to allow taxes to rise on the rich. Otherwise, he has said, the poor and middle class would bear all the burden of deficit reduction.

Some Republican members appear ready to accede.

"The election was a wake-up call," said one veteran Republican in the House. For many members, "everyone they knew hated Obama. Everyone they knew agreed exactly with them. And then we lost."

But other Republicans see a different message.

"If you look at my own election as an example, what voters were saying is they like Obama but they don't trust him on taxes, so they want a check and balance on things," said Representative Tom Latham, Republican of Iowa, who convincingly beat a Democratic incumbent, Leonard L. Boswell. Mr. Obama carried Iowa.

Others representing staunchly conservative districts see no reason to give in, even if the nation as a whole sided with the president on taxes.

"A majority of Americans thought it was just fine to raise taxes on higher income people, but that's more of an emotional response, more 'I'm in pain, I want someone else to pay,"' Mr. Fleming said. But, he added, "How does that solve America's problems? That's counterproductive to go down that road."