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 (21 billion pounds) 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,” the president said at the White House. “This continues to be a make-or-break moment for the middle class … There are going to be some important debates next year.”

Obama heads to vacation in Hawaii with an important political win in his portfolio after he and fellow Democrats prevailed in the message war by backing lower taxes for middle-class Americans in the midst of a fragile economic recovery.

The battle took a toll on House Republicans led by Speaker John Boehner, who were forced to make an embarrassing retreat and agree to a short-term deal Thursday after getting hit by critics on all sides, include their colleagues in the Senate.

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. The fiscal policy debate is 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, newly appointed negotiators are expected to begin work soon on figuring out how to pay for extending the payroll tax cut through 2012.

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.”

‘NOTHING OFF THE TABLE’

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.

Obama scored a victory in the payroll tax struggle over Tea Party conservatives in the House who tried to block the two-month extension. They backed down on Thursday in the face of bipartisan criticism, but they are not going away.

Representative Tim Huelskamp, a first-term Republican, said on CNN that he was disappointed with Republican leadership caving in to pressure and accepting the two-month deal.

Next year could be a rough one for Boehner, the top House Republican, said Norm Ornstein, a scholar at the American Enterprise Institute, a conservative think tank.

Boehner spent 2011 having to negotiate with many of his own party members on just about every major piece of legislation.

Now that House Republicans have had to go along with Democrats in the payroll tax debate, “the idea that this group of angry Tea Party Republicans, who feel betrayed, now will go along or that Boehner will be more capable of defying them is a little bit wrong-headed,” Ornstein said.

Meanwhile, Democrats might be emboldened, believing “they’ve learned to play poker,” he added.

Patrick Griffin, associate director Of American University’s Center for Congressional and Presidential Studies, said House Republicans “overplayed their hand. How they interpret that lesson will be very interesting.”

Any edge conferred on Democrats might be short-lived, however. The 2012 election cycle is just set to kick off with the Iowa Republican presidential caucus on January 3 and a long road lies ahead until voters go to the polls in November.

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.

The $33 billion needed to pay for the two-month extension will be raised by increasing fees charged by housing finance giants Fannie Mae and Freddie Mac for guaranteeing mortgages.

Analysts said the fee hike, which investors will likely pass along to borrowers, could raise financing costs for mortgages, but probably not enough to slow a housing market recovery.

Unemployment benefits set to expire soon were extended as well, while cuts in payments to doctors who treat patients in the government-backed Medicare health insurance program for the elderly were postponed, under the bill signed by Obama.

Also included in it was a Republican initiative aiming to force the administration into fast approval of an oil pipeline opposed by environmentalists and many Democrats. The provision gives Obama 60 days to either approve TransCanada’s Keystone XL pipeline from Canada to Gulf of Mexico facilities in Texas, or declare it not in the national interest.

Obama wants more time to evaluate the environmental impact of routing the pipeline through sensitive areas of Nebraska. The White House has said that if pushed for a decision within 60 days, the administration would be forced to reject the project.

Not extending the payroll tax cut, analysts warned, could have jeopardized the recovery, even risking another recession.

The modest two-month fix drew fire from some businesses that said it will complicate payroll processing and tax planning.

The payroll situation “could get more confusing,” said Robert Gard, an accountant with Gard and LaFreniere LLC in Alpharetta, Georgia. If the tax is not extended at the end of February, businesses will need to reprogram software, he said.