Story highlights The White House says there is time to work out a comprehensive deal

House Republicans say they will not demand spending cuts to offset the payroll tax cut

Republicans concede they had angered voters by pushing that issue late last year

The move, House GOP leaders say, will blunt "Democrats' political games"

In a sharp turnaround, House Republican leaders Monday dropped a key demand that the cost of extending the payroll tax cut be offset by spending cuts elsewhere in the budget.

The decision removes a major obstacle to passage of the tax cut extension for the rest of the year -- a move that has been in question.

Democrats called the GOP decision welcome news -- a "major breakthrough," according to a Democratic aide familiar with the negotiations -- because the tax cut, which would otherwise expire February 29, is a key part of President Barack Obama's economic recovery strategy.

For Republicans, the move trims a thorny political issue. After nearly blocking an extension of the payroll tax cut late last year over concerns about how to pay for it, Republicans acknowledged they had angered voters.

The top three Republican leaders in the House released a statement saying they were prepared to remove the contentious payroll issue from a bill that would also extend unemployment benefits and prevent a fee cut to Medicare doctors -- known as the "doc fix" -- in order to "protect small businesses and our economy from the consequences of Washington Democrats' political games."

"Unfortunately, to date, Democrats have refused virtually every spending cut proposed -- insisting on job-threatening tax hikes on small businesses and job creators -- and with respect to the need for an extension of the payroll tax cut, time is running short," said the statement from House Speaker John Boehner, R-Ohio, House Majority Leader Eric Cantor, R-Virginia, and House Majority Whip Kevin McCarthy, R-California.

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In the past, House GOP leaders have often struggled to get rank-and-file conservative members to go along with their decisions on spending issues -- particularly when related to negotiations with Democrats. The fact that all three leaders issued the statement was seen by aides in both parties as a sign that they expect to be able to pass the bill without conservatives who might break with the leadership.

House Republicans will meet in closed session Tuesday to discuss the proposal, which could be voted on in the House by the end of the week, the leaders said.

Aides in both parties said they expect negotiations to continue on the so-called "doc-fix" and unemployment benefit extension. But they said removing the payroll issue from those talks should make it easier to reach agreement on them.

Those talks would also include potential cost offsets for the payroll tax cut extension, even if it has already passed, the GOP leaders said in their statement.

Sen. John Cornyn of Texas, who heads the Senate Republican election effort, said the decision removes a political hurdle for Republicans as they head into what's expected to be a hard-fought election.

"I think we all recognize that the president's playbook is one to run against Congress and claim we're the problem," he told CNN.

White House Press Secretary Jay Carney insisted Monday there was time for Congress to work out a comprehensive agreement that would extend both the payroll tax cut and unemployment insurance.

However, Carney stopped short of saying Obama would oppose the House proposal to separate the payroll tax provision from the other issues under negotiation.

"This is a hypothetical proposal put out that they said they might do if conversations with folks on Capitol Hill don't progress according to the way they want," Carney told reporters. "Let's just see how this process plays out. Extending unemployment insurance as well as the so-called 'doc fix' is equally important -- certainly very important, and very important for our economy. So the president supports extending all of it, and doing it in a way that is easily achievable if folks put ideological and partisan positions aside."