The White House on Monday threatened to veto a measure that would require congressional approval of a balanced budget amendment to the Constitution before the debt ceiling can be raised.

The GOP-controlled House is expected to vote on such a proposal Tuesday.

A announcement came as a bipartisan effort in the Senate to allow President Obama to raise the federal debt ceiling in exchange for about $1.5 trillion in spending cuts over 10 years gained momentum. Leaders agreed that they would have to act in the next two weeks to avert a potential default by the government.

The growing backing for raising the federal limit on U.S. borrowing sets the stage for a week of largely scripted actions on Capitol Hill, where leaders in both chambers are looking to build support for the plan being crafted by Senate Majority Leader Harry M. Reid (D-Nev.) and Senate Minority Leader Mitch McConnell (R-Ky.).

Republican leaders will first push forward in the House and the Senate with a constitutional amendment to balance the federal budget. The measure is virtually certain to fail in the Senate, which will then take up the debt limit proposal by midweek.

If that clears the Senate, the House is expected to revise the measure, adding a proposal to reduce the deficit by $1.5 trillion over 10 years — savings that would come through cuts to domestic programs but not new tax revenue. The plan would also create a congressional panel that would, by the end of the year, seek to come up with a way of reducing the deficit potentially by trillions more through cuts in entitlements and new tax revenue.

While the debt-limit plan has broad support in the Senate, the prospects in the House are less clear and depend largely on whether Speaker John A. Boehner (R-Ohio) will bring the proposal up for a vote and how many House Democrats would support it, since few Republicans are expected to get behind it.

“At a minimum, Congress has a way to take action and avoid default on the U.S. debt. It’s critical,” Jacob Lew, Obama’s budget director, said Sunday on CNN’s “State of the Union.”

At the same time, the White House will continue to push for as big a deal as possible to cut the deficit, including spending cuts and changes to entitlements as well as increases in tax revenue.

On NBC’s “Meet the Press,” Lew said he hoped the Republicans could compromise with Obama on a big deal. But he did not express optimism. “The question is: Do we have a partner to work with?” he asked.

Informal talks between the White House and Congress over the weekend did not appear to move the two sides significantly closer to a big deal. Leaders face an Aug. 2 deadline to raise the federal debt ceiling or face a potentially damaging government default on the nation’s obligations. They say they need to get a piece of legislation underway by week’s end to clear procedural barriers and raise the debt limit in time.

Most lawmakers were focusing on the new Senate plan, originally proposed last week by McConnell and further developed by Reid. Under the plan, Obama would be able to raise the debt ceiling three times over the next year for a total increase of $2.5 trillion. Congress could also vote on a resolution of disapproval each time, assigning blame to Obama for increasing the nation’s debt.

In addition to the $1.5 trillion in spending cuts, the plan would create a committee of 12 lawmakers, which would issue a report to Congress by the end of the year on how to cut trillions more from federal deficits over the next 10 years. This panel would seek agreement where Obama and Republicans haven’t been able to — primarily over changes to entitlement programs and whether raising new tax revenue should play a key role in cutting the deficit.

“At the end of the day, Republican leaders have made it clear that we will not be the ones to put the government into default,” Sen. Jon Kyl (Ariz.), the chamber’s No. 2 Republican, said on ABC’s “This Week. “Now the House of Representatives has to make its decision about what it will do.”

“We basically have to accept this responsibility and do this job and lead,” said the Senate’s No. 2 Democrat, Richard J. Durbin (Ill.), on CBS’s “Face the Nation.”

Obama and Boehner have both shown a keen interest in a “grand bargain,” but the issue of taxes has proved in­trac­table. Such a deal could still be achieved in the coming weeks, though the prospects have dimmed.

Before taking up the McConnell-Reid plan, the House and Senate will consider the “cut, cap and balance” approach being pushed by Republicans. The House is slated to vote early this week on a balanced-budget amendment to the Constitution that would significantly scale back government spending and make it harder for lawmakers to raise taxes.

Nearly 40 House Republicans have said they would not support an increase in the debt ceiling without such an amendment. But Democrats strongly oppose the measure.

Other Republicans will continue to exert pressure for even bigger cuts. Sen. Tom Coburn (Okla.) will propose on Monday a plan to cut $9 trillion from the federal deficit over 10 years. “The McConnell plan is more of Washington not taking responsibility,” he said Sunday.

Lew expressed confidence that the debt ceiling will be raised despite some GOP objections. “There will be a fringe that believes that playing with Armageddon is a good idea, but I don’t think that’s where the majority will be,” he said.