Their party lost, badly, Mr. Boehner said, and while Republicans would still control the House and would continue to staunchly oppose tax rate increases as Congress grapples with the impending fiscal battle, they had to avoid the nasty showdowns that marked so much of the last two years.
Members on the call, subdued and dark, murmured words of support — even a few who had been a thorn in the speaker’s side for much of this Congress.
It was a striking contrast to a similar call last year, when Mr. Boehner tried to persuade members to compromise with Democrats on a deal to extend a temporary cut in payroll taxes, only to have them loudly revolt.
With President Obama re-elected and Democrats cementing control of the Senate, Mr. Boehner will need to capitalize on the chastened faction of the House G.O.P. that wants to cut a deal to avert sudden tax increases and across-the-board spending cuts in January that could send the economy back into recession. After spending two years marooned between the will of his loud and fractious members and the Democratic Senate majority, the speaker is trying to assert control, and many members seem to be offering support.
“To have a voice at the bargaining table, John Boehner has to be strong,” said Representative Tom Cole of Oklahoma, one of the speaker’s lieutenants. “Most members were just taught a lesson that you’re not going to get everything that you want. It was that kind of election.”
Aides say this is an altered political landscape that Mr. Boehner did not expect. As a result, whether the nation can avoid the so-called fiscal cliff will depend not only on whether Mr. Boehner can find common cause with a newly re-elected, invigorated president, but also whether he can deliver his own caucus.
“I just believe John will have more leeway than in the past Congress,” said Representative Peter T. King, Republican of New York. “The election will matter.”
The divide between Mr. Obama and Mr. Boehner appears wide. In their Saturday addresses, the president demanded immediate House passage of a bill approved by the Senate that would extend the expiring Bush-era tax cuts for households earning under $250,000, while the speaker said raising tax rates on anyone would be unacceptable.
But beneath the posturing, both men were keeping open avenues of negotiation. Mr. Obama was careful to call for more revenue, not higher tax rates, a demand that could be fulfilled by ending or limiting tax deductions and credits, a path Mr. Boehner has accepted.
The question over what to do about the expiring tax cuts would be swept aside if the parties could reach an agreement before then to overhaul the tax code completely — and render obsolete the current structure of six income tax rates, all of which would rise on Jan. 1.
Even so, some Republicans have issued a stern warning to Mr. Boehner that he cannot expect their votes if he makes a deal with 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.
Republican lawmakers and Congressional 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.