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.