WILLIAMSBURG, Va. -- House Republicans will vote next week on a three-month extension of the debt limit, Majority Leader Eric Cantor (R-Va.) said Friday.

Cantor released the following statement at the conclusion of the annual House Republican retreat, where much of the discussion focused on approaching fiscal deadlines:

The first step to fixing this problem is to pass a budget that reduces spending. The House has done so, and will again. The Democratic Senate has not passed a budget in almost four years, which is unfair to hardworking taxpayers who expect more from their representatives. That ends this year.

We must pay our bills and responsibly budget for our future. Next week, we will authorize a three month temporary debt limit increase to give the Senate and House time to pass a budget. Furthermore, if the Senate or House fails to pass a budget in that time, Members of Congress will not be paid by the American people for failing to do their job. No budget, no pay.

The announcement, which was backed by the rest of party leadership, comes a day after House Budget Chair Paul Ryan (R-Wis.) told reporters that Republicans were "discussing the possible virtue of a short-term debt limit extension." Per the new approach, the party is hoping that it can extract spending cuts from President Barack Obama during the course of other looming budget battles -- the automatic sequestration-related cuts that are set to kick in on March 1 and the expiration of the continuing resolution on March 27.

House Speaker John Boehner (R-Ohio) issued his own statement, noting that Republicans "are going to pursue strategies that will obligate the Senate to finally join the House in confronting the government’s spending problem."

"The principle is simple: no budget, no pay," he added.

Boehner maintained that there will be no long-term debt ceiling increase until the Democratic-controlled Senate adopts a budget plan that includes cuts to spending. But the decision to vote on a short-term extension -- which will prevent the government from defaulting on its obligations -- offered a clear indication that Republicans have backed off earlier threats to engage in hostage taking tactics over the debt ceiling, following a series of similar statements from other notable Republicans.

Under the new approach, Republicans are essentially making the case that members will not be paid in the absence of a budget passing through Congress. A House GOP leadership aide explained that if the House were to pass a budget and the Senate did not, House members would still get paid but senators would have their pay withheld. The aide added that member pay would not be changed due to concerns over violating the 27th Amendment, under which "No law, varying the compensation for the services of the Senators and Representatives, shall take effect, until an election of representatives shall have intervened."

The aide also contended that the plan is consistent with the "Boehner Rule" -- which states that a debt ceiling hike must be matched by dollar for dollar spending cuts -- by forcing the Senate to pass a budget for the first time in four years.

In a response to Republicans, a spokesman for Senate Majority Leader Harry Reid (D-Nev.) said the Senate would consider a clean debt ceiling increase if it were to pass the House.

"It is reassuring to see Republicans beginning to back off their threat to hold our economy hostage. 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," Adam Jentleson, Reid's spokesman, said in a statement. "As President Obama has said, this issue is too important to middle class families' economic security to use as a ploy for collecting a ransom. We have an obligation to pay the bills we have already incurred - bills for which many House Republicans voted."

House Minority Leader Nancy Pelosi (D-Calif.) poured cold water on the Republicans' proposal, calling for a "clean" debt ceiling hike. "This proposal does not relieve the uncertainty faced by small businesses, the markets and the middle class. 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," said her spokesman, Drew Hamill.

The White House responded by saying it was "encouraged" that Republicans are moving away from earlier debt ceiling threats. Press Secretary Jay Carney issued the following statement:

The President has made clear that Congress has only two options: pay the bills they have racked up, or fail to do so and put our nation into default.  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. Congress must pay its bills and pass a clean debt limit increase without further delay. And as he has said, the President remains committed to further reducing the deficit in a balanced way.