“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 Wednesday’s conference call, their ranks slightly 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, and those included often-rebellious conservatives like Representatives Phil Gingrey of Georgia and Virginia Foxx of North Carolina.

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 reform legislation, in a blunt acknowledgment of his party’s weakness among Hispanic voters — got immediate pushback from some members, including Mr. Fleming and Representative Steve King of Iowa.

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.