WASHINGTON (AP) — House Republicans on Thursday caved to demands by President Barack Obama, congressional Democrats and fellow Republicans for a short-term renewal of payroll tax cuts for all workers. The breakthrough almost certainly spares workers an average $20 a week tax increase Jan. 1.

After days of wrangling that even Speaker John Boehner acknowledged “may not have been politically the smartest thing in the world,” the Ohio Republican abruptly changed course and dropped demands for immediate holiday season talks with the Senate on a full-year measure that all sides said they want. Senate leaders had insisted on the two-month extension to buy time for talks next year.

The House and Senate plan to act on the two-month extension Friday.

House Republicans were under fire from their constituents and GOP establishment figures incensed that they would risk losing the tax cut issue to Democrats at the dawn of the 2012 presidential and congressional election year. House GOP arguments about the legislative process and the “uncertainty” a two-month extension would mean for business were unpersuasive.

“In the end House Republicans felt like they were reenacting the Alamo, with no reinforcements and our friends shooting at us,” said Rep. Kevin Brady, R-Texas.

The compromise legislation would renew the tax break through Feb. 29, along with jobless benefits and a “fix” to prevent doctors from absorbing a big cut in Medicare payments. Its $33 billion cost would be covered by an increased fee on mortgages backed by Fannie Mae, and Freddie Mac.

The developments were a clear win for Obama. The payroll tax cut was the centerpiece of his three-month campaign-style drive for jobs legislation that seems to have contributed to an uptick in his poll numbers — and taken a toll on those of congressional Republicans.

“Because of this agreement, every working American will keep his or her tax cut – about $1,000 for the average family,” Obama said in a statement. “That’s about $40 in every paycheck. And when Congress returns, I urge them to keep working to reach an agreement that will extend this tax cut and unemployment insurance for all of 2012 without drama or delay.”

If the cuts had expired as scheduled, 160 million workers would have seen a 2 percentage point increase in their Social Security taxes. And up to 2 million people without jobs for six months would start losing unemployment benefits averaging $300 a week.

The GOP retreat ends a tense standoff in which Boehner’s House Republicans came under great pressure to agree to the short-term extension passed by the Senate on Saturday. The speaker was initially open to the idea, but rank-and-file Republicans revolted, and the House instead insisted on immediate talks on the year-long measure passed by the House, which contains curbs to unemployment insurance and other ideas backed by conservatives — as well as deeper spending cuts to pay for the full-year cost.

After Senate leaders tried but failed to match the House’s goal for a full-year pact, the chamber on Saturday instead gave sweeping approval for the two-month extension of the payroll tax cut, jobless benefits and doctors’ Medicare fees that otherwise would have been cut 27 percent. The House had just days before passed a full-year extension that included a series of conservative policy prescriptions unpalatable to Obama and congressional Democrats.

Obama, Republicans and congressional Democrats all said they preferred a one-year extension but the politics of achieving that eluded them. All pledged to start working on that in January.

“Has this place become so dysfunctional that even when we agree to things we can’t do it?” Obama asked. “Enough is enough.”.

The top Senate Republican, Mitch McConnell of Kentucky, was a driving force behind Thursday’s agreement, imploring Boehner to accept the deal that McConnell and Senate Democratic Leader Harry Reid had struck last week and passed with overwhelming support in both parties.

“There remain important differences between the parties on how to implement these policies, and it is critical that we protect middle-class families from a tax increase while we work them out,” Reid said after Boehner’s announcement.

The breakthrough emerged as a firewall erected by tea party-backed House Republicans crumbled Thursday.

“I don’t think that my constituents should have a tax increase because of Washington’s dysfunction,” said freshman Rep. Sean Duffy, R-Wis.

The Republican establishment, too, put new pressure on House Republicans to compromise.

The 2008 GOP presidential nominee, John McCain, former Bush administration confidant Karl Rove and The Wall Street Journal editorial page were among conservative voices urging House Republicans to retreat.

Just hours before he announced the breakthrough, Boehner had made the case for a year-long extension. But on a brief late afternoon conference call, he informed his colleagues it was time to yield.

“He said that as your leader, you’ve in effect asked me to make decisions easy and difficult and I’m making my decision right now,” said Rep. Jack Kingston, R-Ga., paraphrasing Boehner’s comments.

Kingston said the conference call lasted just minutes and Boehner did not give anyone time to respond.

There was still carping among tea party freshmen upset that GOP leaders had yielded.

“Even though there is plenty of evidence this is a bad deal for America … the House has caved yet again to the president and Senate Democrats,” said Rep. Tim Huelskamp, R-Kan. “We were sent here with a clear set of instructions from the American people to put an end to business as usual in Washington, yet here we are being asked to sign off on yet another gimmick.”

Almost forgotten in the firestorm is that McConnell and Boehner had extracted a major victory last week, winning a provision that would require Obama to make a swift decision on whether to approve construction of the Keystone XL oil pipeline, which would bring Canadian oil to the U.S. and create thousands of construction jobs. To block the pipeline, Obama would have to declare that is not in the nation’s interest.

Obama wanted to put the decision off until after the 2012 election.

House Republicans did win one concession in addition to a promise that Senate Democrats would name negotiators on the one-year House measure: a provision to ease concerns that the 60-day extension would be hard for payroll processing companies to implement.