WASHINGTON — House Republican leaders Friday offered President Barack Obama a three-month reprieve to a looming, market-rattling debt crisis, backing off demands that any immediate extension of the government’s borrowing authority be accompanied by stiff spending cuts.

The retreat came with a caveat aimed at prodding Senate Democrats to pass a budget after almost four years of failing to do so: a threat to cut off the pay of lawmakers in either House or Senate if their chamber fails to pass a budget this year. House Republicans have passed budgets for two consecutive years.

The idea got a frosty reception from House Democrats but a more measured response from the White House and Democratic Senate Majority Leader Harry Reid of Nevada.

Republicans hadn’t settled on full details, but the measure would give the government about three more months of borrowing authority beyond a deadline expected to hit as early as mid-February, No. 2 House Republican Eric Cantor of Virginia said Friday.

The legislation wouldn’t require immediate spending cuts as earlier promised by GOP leaders like Speaker John Boehner of Ohio. Instead, it’s aimed at forcing the Democratic-controlled Senate to join the House in debating the federal budget.

“We are going to pursue strategies that will obligate the Senate to finally join the House in confronting the government’s spending problem,” Boehner told GOP lawmakers at a retreat in Williamsburg, Va. “The principle is simple: ‘no budget, no pay.”’

But the move ran into opposition from House Democrats, including leader Nancy Pelosi of California, who called it a gimmick because it would set up another potential confrontation in just a few months. Votes from Democrats may be needed to help pass the measure if GOP conservatives opposed to any increase in the debt limit withhold their support.

“This proposal does not relieve the uncertainty faced by small businesses, the markets and the middle class,” said Pelosi spokesman Drew Hammill. “This is a gimmick unworthy of the challenges we face and the national debate we should be having. The message from the American people is clear: no games, no default.”

But Senate Democrats and the White House were more cautious and sounded encouraged that Republicans seemed to be beating a tactical retreat.

“We are encouraged that there are signs that congressional Republicans may back off their insistence on holding our economy hostage to extract drastic cuts in Medicare, education and programs middle-class families depend on,” said White House Press Secretary Jay Carney in a statement. “Congress must pay its bills and pass a clean debt-limit increase without further delay.”

“It is reassuring to see Republicans beginning to back off their threat to hold our economy hostage,” said Reid spokesman Adam Jentleson. “If the House can pass a clean debt-ceiling increase to avoid default and allow the United States to meet its existing obligations, we will be happy to consider it.”

But in Washington-speak, a “clean” debt limit increase means a stand-alone measure without additional items — like the “no budget, no pay” idea — attached. Jentleson said Reid and his fellow Senate Democrats have yet to decide how they’ll respond to the measure.

The “no budget, no pay” idea is backed by No Labels, a group started about two years ago by both Democrats and Republicans in hopes of easing the partisanship and gridlock that has engulfed Washington. Sponsors in Congress include Rep. Jim Cooper, D-Tenn., and Sen. Dean Heller, R-Nev.

The Democratic-controlled Senate passed a similar idea in 2011 when unanimously adopting a measure to deny pay to members of Congress and the president if the government shuts down for lack of an agency funding bill. But top lawmakers like Judiciary Committee Chairman Patrick Leahy, D-Vt., have argued that the idea violates a provision of the Constitution that says Congress can’t change its pay until an election has passed.

At the same time, while Democrats like Pelosi and allies like Rep. Chris Van Hollen of Maryland protest the idea of a short-term debt increase in the government’s $16.4 trillion debt cap, they orchestrated comparable short-term debt relief when they controlled Congress in 2009.

GOP leaders, meanwhile, have been grappling with how to gain leverage in their battles with Obama over the budget. Boehner successfully won about $2 trillion in spending cuts as a condition of increasing the government’s borrowing cap in 2011.

Obama, however, was dealt a stronger hand by his re-election in November and successfully pressed through a 10-year, $600 billion increase on upper-bracket tax payers earlier this month.

Other choke points remain, including sharp, across-the-board spending cuts that would start to strike the Pentagon and domestic programs alike on March 1 and the possibility of a partial government shutdown with the expiration of a temporary budget measure on March 27.

Failing to meet those deadlines would have far less serious consequences than defaulting on U.S. obligations like payments to bondholders, Social Security recipients and myriad other commitments when the government confronts a cash crisis and can no longer borrow to make payments. That could cause a meltdown in financial markets and would inflame voters already disgusted with Congress.

Under Congress’ arcane budget procedures, a congressional budget resolution is a nonbinding measure that tries to set parameters for future legislation setting agency budgets and curbing federal benefit programs like Medicare.

Boehner has previously invoked a promise that any increase in the government’s borrowing cap would be matched, dollar for dollar, by spending cuts or “reforms” that could include curbs on the long-term growth in retirement programs such as Medicare. Friday’s announcement did not repeat that specific promise.

“Before there is any long-term debt limit increase, a budget should be passed that cuts spending,” Boehner said. “The Democratic-controlled Senate has failed to pass a budget for four years. That is a shameful run that needs to end, this year.”

The measure picked up support from key GOP conservatives, including the current and former chairmen of the Republican Study Committee, a powerful group inside the House GOP.

“In order to allow time for the Senate to act, next week’s bill will extend the debt limit for three months,” the Study Committee said Friday in a statement. “This is a necessary first step as we work to halt the decline of America and puts the focus where it belongs: on the Senate who has failed to do their jobs to pass a budget for more than three years.” The statement was issued by RSC Chairman Steve Scalise, R-La., and former chairmen, Jim Jordan, R-Ohio, Tom Price, R-Ga., and Jeb Hensarling, R-Texas.

Obama’s budget is due early next month but is expected to be released several weeks later.