WASHINGTON — Courting confrontation and compromise alike, House Republicans shrugged off President Obama’s threat to veto legislation to cut federal spending by trillions of dollars on Monday while simultaneously negotiating with him over more modest steps to avert a potential government default.

The Republican bill demands deep spending reductions and congressional approval of a balanced budget amendment to the Constitution in exchange for raising the nation’s debt limit. But Obama will veto it if it reaches his desk, the White House said, asserting the legislation would “lead to severe cuts in Medicare and Social Security” and impose unrealistic limits on education spending.

In response, GOP lawmakers said they would go ahead with plans to pass the bill today. “It’s disappointing the White House would reject this common-sense plan to rein in the debt and deficits that are hurting job creation in America,” said Speaker John Boehner, R-Ohio.

By contrast, neither the administration nor congressional officials provided substantive details on an unannounced meeting that Obama held Sunday with the two top House Republican leaders, Boehner and Majority Leader Eric Cantor of Virginia.

Obama said late Monday the two sides were “making progress.”

Several Republicans said privately that the decision to vote on veto-threatened legislation is paradoxically designed to clear the way for a compromise. They said conservatives would have a chance to push their deep spending cuts through the House, and then see the measure quickly die either in the Democratic-controlled Senate or by veto.

Barring action by Congress to raise the $14.3 trillion debt limit, the Treasury will be unable to pay all the government’s bills that come due beginning Aug. 3, two weeks from Wednesday. Administration officials, Federal Reserve Chairman Ben Bernanke and others say the result could be a default that inflicts serious harm on the economy.

In a gesture underscoring the significance of the issue, Majority Leader Harry Reid, D-Nev., announced the Senate will meet each day until it is resolved, including on weekends.

The two-pronged approach pursued by the House GOP follows the collapse of a weeks-long effort to negotiate a sweeping bipartisan plan to cut into future deficits. The endeavor foundered when Obama demanded that tax increases on the wealthy and selected corporations be included alongside cuts in benefit programs, and Republicans refused.

The failure of that effort also reflects the outsized influence exerted by 87 first-term Republicans, many of them elected last fall with tea party backing.

As late as last Thursday, Republican leaders held a news conference to tout plans to vote this week on a proposed balanced-budget amendment to the Constitution.

But the same senior Republicans emerged Friday from a closed-door meeting of the rank and file to say the House would instead vote on an alternative – dubbed by its advocates as “cut, cap and balance.” No date has been set for a vote on the constitutional amendment itself.