Updated: 6:38 p.m. ET
House Speaker John Boehner said Thursday that his fellow GOP congressmen have agreed on a deal to extend for two months the payroll tax cuts that would have expired at the end of the year. The announcement ends yet another episode of political brinksmanship in Washington that has contributed greatly to Congress' abysmal approval ratings.
The agreement allows the House to adopt the Senate's version of the two-month extension, albeit with some face-saving tweaks. The extension would begin on Jan. 1. In addition to language about jobless benefits, the agreement includes a provision expediting the review of the controversial.
Boehner said he expects a vote to pass the legislation will occur "before Christmas."
"I think our members waged a good fight," Boehner said. "We were able to come to an agreement. We were able to fix what came out of the Senate."
There is a chance the deal could get derailed when Boehner seeks a "unanimous consent" vote on the deal, which would require every single GOP House member - even the angry ones - to agree. If any single congressman objects, that could require the whole chamber to reconvene after Christmas for a formal vote.
CBS News correspondent Nancy Cordes reports that, as they had been deserted by Senate Republicans and derided by Democrats, House Republicans believed they had no choice but to back down on their earlier objections to the deal.
The new bill will keep the payroll tax rate at its current 4.2 percent instead of the previous 6.2 percent. It also will extend unemployment benefits, continuing to give people who've been out of work up to 99 weeks of unemployment checks.
As part of Thursday's agreement, House Republicans extracted a promise that the Senate will appoint negotiators -- just as they have -- to immediately work out a year-long deal when Congress returns in January.
A House GOP aide told CBS News earlier in the day that the House would accept a new bill reflecting the two-month extension previously passed in the Senate, but would add language protecting small businesses from costly new reporting requirements in the Senate bill.
President Barack Obama said he welcomes a deal on extending a payroll tax cut and congratulating Congress for ending its "partisan stalemate."
The president issued a statement Thursday evening moments after Boehner announced that House Republicans were reversing course and accepting a two-month extension agreed to by the Senate and supported by the president.
Obama says the deal, which also extends unemployment benefits, is good news just in time for the holidays and the right thing to do for American families and the economy.
And he is thanking Americans who pressured Congress to get it done.
Senate Minority Leader Mitch McConnell, whose urgings may have pushed House Republicans to compromise, said: "With today's agreement between the Speaker and Leader Reid, working Americans can breathe a sigh of relief knowing that their taxes will not go up at the end of the year and that the President will have to finally decide on whether to move forward on a pipeline project that would create thousands of American jobs."
Boehner met with House conferees and Rep. Eric Cantor, R-Va., Thursday afternoon, and they gave the speaker their blessing for him to reach an immediate resolution with Reid. Boehner then appointed Rep. Dave Chairman Camp, R-Mi., to hammer out the details of the legislative fix to the language in the Senate bill with Democratic Senator Max Baucus.
This afternoon, Boehner informed House leaders over the phone that he intended to reach out to Reid for a possible deal, and proceeded with steps aimed at setting up the conference call with House Republicans.
Reid accepted Boehner's proposal, and the House is scheduled to be in pro forma session at 10 a.m. Friday -- which means the House could pass it by unanimous consent.
House Republicans had argued that the Senate bill - which was negotiated in a bipartisan effort by leaders Mitch McConnell, R-Ky., and Harry Reid, D-Nev., and which sailed through the chamber last weekend with broad bipartisan support - is a short-term fix for a long-term problem.
As late as Thursday morning, Boehner appeared to beon the matter, even while fellow Republican McConnell urged House lawmakers to pass the Senate bill.