After a week of refusing to accept the extension of the payroll tax cut that their own party helped negotiate, Republicans in the House of Representatives have finally agreed to pass the bill, according to the New York Times.

Under a deal reached between House and Senate leaders, the House will now approve as early as Friday the two-month extension of a payroll tax holiday and unemployment benefits approved by the Senate last Saturday, and the Senate will appoint members of a House-Senate conference committee to negotiate legislation to extend both benefits through 2012.

The extension means that the percentage taken out of an employee’s paycheck to pay for Social Security will stay at the current rate of 4.2% until March. If the Republicans had not agreed to extend the tax cut, the rate would have increased to 6.2% starting January 1st. By the time the tax cut expires in March, Democrats and Republicans hope to have negotiated a long-term extension of the pay roll tax cut that will stay in effect for all of next year.

The surrender of House Republicans ends a remarkable week-long mutiny led by Speaker of the House John Boehner (R-OH) against a bipartisan compromise bill negotiated by Senate Majority Leader Harry Reid (D-NV) and Senate Minority Leader Mitch McConnell (R-KY). Though the bill had the support of both Republicans and Democrats in the Senate, a rebellious group of House Republicans objected to the bill.

They wanted to pass an extension of the cut for a full year and pay for it by cutting Medicare and unemployment benefits. Unsurprisingly, Democrats objected to this idea, which is why it didn’t make it into the compromise bill. The House Republicans decided to dig in their heels, refusing to pass the compromise bill. As Speaker Boehner later admitted, this was not the best idea.

After his conversation with lawmakers, the speaker conceded to reporters that it might not have been “politically the smartest thing in the world” for House Republicans to put themselves between a tax cut and the 160 million American workers who would benefit from it, and to allow President Obama and Congressional Democrats to seize the momentum on the issue.

President Obama, meanwhile, celebrated the compromise for the help it will bring middle-class Americans.

“This is good news, just in time for the holidays,” he said in a statement. “This is the right thing to do to strengthen our families, grow our economy, and create new jobs. This is real money that will make a real difference in people’s lives.”