By Jennifer Steinhauer and Jackie Calmes

WASHINGTON — Bowing under intense pressure from members of their own party to end the politically damaging impasse over a payroll tax holiday, House Republican leaders agreed Thursday to accept a temporary extension of the tax cut, beating a hasty retreat from a showdown that Republicans increasingly saw as a threat to their election opportunities next year.

Under a deal reached between House and Senate leaders — which Speaker John A. Boehner presented to the rank and file in an evening conference call — House members would accept the two-month extension of a payroll tax holiday and unemployment benefits approved by the Senate last Saturday, while the Senate would appoint members of a House-Senate conference committee to negotiate legislation to extend both benefits through 2012.

Mr. Boehner said in a Capitol Hill news conference Thursday that if the compromise was not approved in the House by unanimous consent on Friday, as planned, he would “absolutely’’ call the House back into session for a vote next week. The House is in pro forma session and can make such a move if no one objects. The Senate is expected to do the same.    

“It may not have been politically the smartest thing in the world,’’ Mr. Boehner said. “But let me tell you what: I think our members waged a good fight.’’     

Though the agreement extricated House Republicans from a political box, Mr. Boehner said: “I don’t think it’s any time for celebration. Our economy is struggling.’’

House Republicans — who rejected an almost identical deal on Tuesday on the House floor — caved in under the political rubble that accumulated over the week, much of it from members of their own party, who worried the blockade would do serious damage to the party brand heading into an election year. The new deal makes minor adjustments to make it easier for small businesses with temporary new caps on the wages that are subject to the tax relief.

The agreement ended a partisan fight that threatened to keep Congress — and President Obama — in town through Christmas and was just the latest of the fierce fights between House conservatives, the president and the Democratic-controlled Senate. But this one seemed to end in a clear victory for Mr. Obama and the Democrats, at least for now.

The push to find a resolution was touched off Thursday by Senator Mitch McConnell of Kentucky, the Republican leader, who had negotiated the two-month extension and called on the House to accept a temporary continuation of the tax hike and extended unemployment pay as long as Senate Democrats committed to opening negotiations quickly over a yearlong agreement.

“House Republicans sensibly want greater certainty about the duration of these provisions, while Senate Democrats want more time to negotiate the terms,” Mr. McConnell said in a prepared statement. “We can and should do both. Working Americans have suffered enough from the president’s failed economic policies and shouldn’t face the uncertainty of a New Year’s Day tax hike.”

Just hours after Mr. McConnell released his statement, House freshmen began to crumble.

“I’m calling on G.O.P. leadership to immediately bring up the Senate’s two-month extension for an up or down vote,” said Representative Sean Duffy of Wisconsin, who voted against the deal earlier in the week. “Middle-class families deserve a Congress that will rise above the squabbling and ensure their taxes don’t go up right after Christmas.”

On the Web site of Representative Rick Crawford of Arkansas were two statements, one from Tuesday proclaiming his vote against a Senate bill, and a new message on Thursday in a letter to Mr. Boehner. “We are now in a position that requires all options to be on the table, that requires Republicans to not only demand a willingness to compromise, but to offer it as well,” Mr. Crawford wrote in the letter to Mr. Boehner. “More often than not an ‘all or nothing’ attitude produces nothing.”

Mr. McConnell’s statement gave a lifeline of sorts to House Republicans by opening the door to a change in the length of the extension — some Republicans say a three-month fix would be easier for employers to handle — that sought to find a face-saving way out of the conflict. Many Republicans had acknowledged it had the capacity to harm their party in the opening days of an election year that would pick a president and decide control of the divided Congress. Many Senate Republicans and other party members expressed deepening worry that the fight was whittling away at their chance to take back the Senate, remove Mr. Obama and even hold their significant majority in the House.

At the same time, some of senior members of the Republican Party — ranging from Senator John McCain of Arizona to prominent analysts like Karl Rove — see the possibility of a Republican-controlled Congress next year and even a Republican in the White House, and are dismayed by what they see as the suicidal tendencies of the newest members of the House, who they feel should put the party’s endurance through 2012 over perfect legislative goals.

“I don’t care about my re-election effort,” said Representative Tom Reed of New York, a conferee appointed by Mr. Boehner to negotiate a deal. “I came here to do what’s right for America.”

The deal also offered Mr. Boehner something that has often eluded him this year: a sense of consequences for his rowdy freshmen members who have helped Republicans push their cost-cutting agenda further than the party could have ever hoped, but with high cost to how it is perceived.

Earlier in the day, Mr. Obama was flanked by 16 unidentified Americans who had responded to a White House campaign soliciting responses to its Web site, Twitter and Facebook about what they would sacrifice if their take-home pay was reduced by $40 each paycheck, or $20 a week, the average tax break for a family making $50,000 a year.