By Richard Cowan and Rachelle Younglai

WASHINGTON (Reuters) - President Barack Obama signed into law a two-month payroll tax cut extension on Friday, capping a year of fierce partisan combat over taxes and spending that will resume in January and play heavily in the 2012 elections.

The Senate and the House of Representatives, by voice votes in chambers nearly emptied for the holidays, passed a $33 billion bill to keep the payroll tax rate at 4.2 percent through February. It had been scheduled to increase on January 1 to 6.2 percent. Obama swiftly signed the bill.

"We have a lot more work to do," Obama said in remarks at the White House before heading to Hawaii for vacation. "This continues to be a make-or-break moment for the middle class in this country ... There are going to be some important debates next year."

The temporary fix lets lawmakers lower the curtain, for now, on a year of political deadlock that in the end produced only a series of inconclusive truces in a fiscal policy debate set to rage straight through the 2012 election season and beyond.

While Congress is on a long winter break now and does not return to full swing until late January, the newly appointed negotiators on a year-long payroll tax cut deal are expected to begin work soon.

Republicans have sought a continued freeze on federal worker pay and cuts in Medicare benefits for the wealthy. Democrats have rejected both ideas while proposing a surtax on the wealthy to cover the extension's cost. Republicans reject this.

Both sides have been open to cutting federal workers' pension benefits. There also were last-minute Senate negotiations last week on possibly ending some tax breaks for the wealthy, such as a small one involving corporate jets.

Minutes after the bipartisan deal was passed by Congress, the bickering that has come to dominate Capitol Hill resumed.

Republican Representative Tom Price, a leader of House conservatives, immediately criticized the short-term extension, calling it a "two-month punt" and saying it would not have been needed if Senate Majority Leader Harry Reid, a Democrat, and Obama had "been willing to do their job today."

In a sign that the battle is far from over, Reid signaled that Democrats could renew their push for a surtax on wealthier Americans. Democrats had dropped that demand during the year-end negotiations that produced the two-month deal.

"There is nothing off the table," he said.

The payroll tax funds the Social Security retirement pension system. If it had been allowed to rise, the increase would have hit the wallets of 160 million working Americans.

Obama scored a political victory in the payroll tax struggle over Tea Party conservatives in the House who tried to block the two-month extension. They backed down late on Thursday in the face of ferocious bipartisan criticism.

(Reporting by Richard Cowan, Rachelle Younglai, Patrick Temple-West, Margaret Chadbourn and Ayesha Raschoe. Writing By Kevin Drawbaugh; Editing by Ross Colvin, Eric Beech and Bill Trott)