In a major tactical shift, House Republican leaders Monday said they would sign off on a payroll tax cut extension that is not paid for, marking an attempt to both pressure Democrats and get the issue behind them.

Bruised from a months-long battle to pay for the $100 billion payroll tax holiday, Republicans are acknowledging that they would rather give in on a straight extension than fight on for spending cuts that Senate Democrats will not accept.

In doing so, they could also deprive President Barack Obama and the Democrats of a political weapon that has been used to great effect against Republicans: that the GOP is holding up a tax cut for 160 million Americans.

A bill from GOP leaders could come to the House floor as soon as Wednesday. Though Democrats immediately groused, Republicans are hoping they will find such an offer impossible to shun.

House Minority Leader Nancy Pelosi (D-Calif.) said in a statement that although she supports an extension that is not offset, she is concerned about decoupling the proposal from an extension of long-term unemployment insurance benefits and a proposal to halt a scheduled cut to reimbursements for doctors who treat Medicare patients.

“There is no reason all three of these priorities cannot proceed at the same time as both the House and Senate agreed,” Pelosi said in a statement.

Rep. Sander Levin (D-Mich.), a conferee, said decoupling the proposals is “completely irresponsible.”

Nevertheless, Rep. Chris Van Hollen said that despite his concerns about breaking up the package, he believes there would be widespread support within the House Democratic Caucus for just a payroll tax holiday extension.

“I support a straight payroll tax cut extension,” said the Maryland Democrat, a conferee who is close to Democratic House leadership. “If they’ve changed their position, with respect to offsetting the payroll tax cut as they’ve proposed, that would be a positive development.”

GOP leaders must also get their conservative Members on board, however. The House Republican Conference will meet at 6 p.m. to discuss the plan, and aides acknowledge it likely will not thrill them.

Still, Republican aides said, the Conference will probably back the plan. Giving GOP lawmakers cover, Heritage Action for America released a statement Monday stating that “it is past time to move beyond this issue” and that this move would “deny obstinate Senate Democrats the ability to play partisan games.”

House Ways and Means Chairman Dave Camp (R-Mich.), co-chairman of the conference committee, said in a statement that he supports the GOP proposal and that conference committee talks will continue.

If the House approves the measure, it would set up a chess match with Senate leaders on how to resolve the unemployment and Medicare doc fix issues.

Senate Majority Leader Harry Reid (D-Nev.) would face two basic choices. He could take up the House-passed bill, amend it to include the unemployment and doc fix provisions, and send it back to the House. Or he could pass the clean bill and then work on separate legislation for the other issues.

Facing a possible filibuster and a Senate Republican Conference that has tried to work in lock step with its House counterpart, Reid could face serious difficulties if he attempts to amend the clean bill. The payroll tax cut extension has been a top priority for the White House for months and at the center of Congressional Democrats’ messaging, much more than unemployment insurance has been.

By moving the payroll tax cut on its own, sources said, Republicans are trying to ensure that they don’t get stuck in the same situation they found themselves in last December: blamed for failure. If Reid kills the clean bill in the Senate, the tables could turn.

If Senate Democrats move separately on a bill after passing the tax cut, they could face an easier path, according to sources familiar with Senate procedure who spoke on the condition of anonymity so that they would not jeopardize potential progress on a compromise.

On unemployment benefits, Democrats could draft legislation that would represent a compromise position between current law and the House-passed plan approved last year. The House legislation cut the weeks of eligibility for benefits to 59 from 99 and included a series of other changes, such as enabling states to drug test recipients and mandate jobless Americans without high school diplomas to earn their equivalency degrees.

Democrats could put forth a bill that includes an eligibility limit of 75 weeks of coverage — a number in the ballpark of what was being negotiated by Reid and Senate Minority Leader Mitch McConnell (R-Ky.) in full-year negotiations that collapsed before Christmas. According to projections, 10 months of unemployment benefits for that duration would cost about $28 billion. The Senate then could use commonly discussed offsets, such as spectrum auctions — which the Bowles-Simpson deficit reduction panel estimated to bring in $55 billion from 1993 to 2010 — to pay for the extension.

In 2010, Republican Sens. Olympia Snowe (Maine), Susan Collins (Maine) and Scott Brown (Mass.), in addition to now-retired Sen. George Voinovich (Ohio), voted multiple times for unpaid-for jobless benefits extensions. Snowe and Brown are up for re-election. Just last week, Sen. Dean Heller (R-Nev.), who is in a competitive race this November, sent a letter to Camp calling for an extension of current law in his state. Other GOP Senators facing tough re-elections, such as Dick Lugar (Ind.), could face pressure to support a fully offset bill, according to Republican aides.