The White House formally threatened Monday to veto a Republican measure requiring congressional approval of a balanced-budget amendment to the Constitution before the nation’s debt ceiling can be raised.

House Republican leaders denounced the veto threat and said they would go ahead with a scheduled vote Tuesday on the proposal, which would impose strict new spending caps and require that Congress give the balanced-budget amendment the two-thirds vote necessary to send it to the states for ratification before the debt limit could be raised.

In the Senate, Majority Leader Harry M. Reid (D-Nev.) announced that the chamber would not recess until Congress passes a deal to raise the country’s $14.3 trillion borrowing limit.

“The Senate has no more important task than making sure the United States does not fail to pay our bills for pre-existing obligations like Social Security for the first time in our history,” Reid said in a statement Monday afternoon. “To ensure that we meet this responsibility, the Senate will stay in session every day, including Saturdays and Sundays, from now until Congress passes legislation that prevents the United States from defaulting on our obligations.”

Reid’s move came as negotiations over the debt ceiling entered their final two weeks. The White House has said that leaders must agree on a deal by Friday to give both chambers time to move the legislation before an Aug. 2 deadline, when it says the government would begin to default on its debt obligations.

Reid and Senate Minority Leader Mitch McConnell(R-Ky.) have been making progress on a deal that would allow the debt ceiling to be raised in return for about $1.5 trillion in spending cuts over 10 years. The plan would also call for the formation of a bipartisan 12-member committee to identify additional deficit savings by the end of the year. Leaders in both chambers have not shut the door to such a deal, although rank-and-file Republicans have signaled strong opposition.

In announcing President Obama’s threat to veto the House GOP’s “Cut, Cap and Balance Act of 2011,” the White House said it would set up a “false and unacceptable choice” between failing to lift the nation’s borrowing limit by Aug. 2, resulting in the country’s first default, or passing a balanced-budget amendment that would require draconian spending cuts in Medicare, Social Security and other federal programs in future years.

“Neither setting arbitrary spending levels nor amending the Constitution is necessary to restore fiscal responsibility,” the Office of Management and Budget said in a statement. “Increasing the federal debt limit, which is needed to avoid a federal government default on its obligations and a severe blow to the economy, should not be conditioned on taking these actions.”

The statement added: “Instead of pursuing an empty political statement and unrealistic policy goals, it is necessary to move beyond politics as usual and find bipartisan common ground.”

In a subsequent Rose Garden speech announcing his nominee to head the Consumer Financial Protection Bureau, Obama drove home that point. “We can’t let politics stand in the way of doing the right thing in Washington,” he said. “We can’t stand in the way when it comes to doing the right thing on deficits.”

Asked by a reporter at the end of his remarks whether he had made any progress in talks Sunday with House Speaker John A. Boehner (R-Ohio), Obama replied simply, “We’re making progress.”

In response to the White House veto statement, Boehner said, “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.”

He charged in a statement that the White House “obviously isn’t serious about making the same tough choices” that American families have to make. “While the House is once again acting responsibly, the administration still won’t say what cuts it’s willing to make to end Washington’s spending binge and the economic uncertainty it’s creating,” Boehner said. “ This unfortunate veto threat should make clear that the issue is not congressional inaction, but rather the president’s unwillingness to cut spending and restrain the future growth of our government. If we are going to raise the debt limit and avoid default, the White House must be willing to demonstrate more courage than we have seen to date.”

Boehner said the House would “proceed as planned with its vote on the Cut, Cap and Balance Act.”

Republicans have insisted that a balanced budget amendment would spare the country similar debates in the future by mandating spending discipline. Under the measure the House will consider Tuesday, spending caps would be applied over the 10 years that match outlays included in a budget written by Rep. Paul Ryan (R-Wis.) and passed by the House earlier this year.

But the bill would also require passage of a Constitutional amendment that would mandate spending caps and require a two-thirds vote of Congress for any future tax increase.

“Let’s let the states and the American people decide,” said Sen. Jim DeMint (R-S.C.) on NBC’s “Meet the Press” on Sunday. “It wouldn’t happen until about 10 years out, but it gives us time to fix our tax code, to fix Social Security and Medicare. And that’s what we have to do.”

Obama has continued to push Congress to accept a grand bargain that would reduce the debt by about $4 trillion over 10 years. He has said congressional leaders need to reach an agreement that would lead to a balanced budget, rather than pass a constitutional requirement that future lawmakers do so. 

“We don’t need a constitutional amendment to do our jobs,” Obama told a news conference Friday.

Democrats are watching the vote warily, even though such a House-passed measure is unlikely to make it through the Senate. They hope that a recorded House vote on the issue could provide conservatives some cover to make a tough compromise and raise the debt ceiling next week.

But they also worry that Tuesday’s vote may not be enough to satisfy some staunch conservatives.

Meanwhile, growing support for the McConnell-Reid plan to raise the debt ceiling 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 proposal.

If the debt-limit plan 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.

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

“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.

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 remain at odds — 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.”

Other Republicans were exerting pressure for even bigger cuts that those envisioned in any of the plans. Sen. Tom Coburn (R-Okla.) planned to propose a plan Monday 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.

“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.

Staff writer William Branigin contributed to this report.