WASHINGTON — Struggling to avert an unprecedented national default, congressional leaders jettisoned negotiations on a sweeping deficit-reduction package Friday despite a plea from President Barack Obama to “do something big” to stabilize America’s finances.

Instead, lawmakers embarked on competing fallback plans as a critical Aug. 2 deadline neared, a House Republican version given little chance of success, even by some supporters, and a bipartisan Senate approach holding out more promise to avert what Obama called financial “Armageddon.”

Late Friday, the Treasury Department announced it was resorting to the final steps in an unusual series designed to avoid exceeding the current $14.3 trillion debt limit. Numerous officials have cautioned that a default will occur if the limit is not increased by Aug. 2, warning also of a calamitous effect on a national economy struggling to recover from the worst recession in decades..

At the behest of conservatives, House Republicans announced plans to vote next week on legislation to permit more borrowing automatically if Congress approves a balanced-budget constitutional amendment. Senate approval of that amendment seemed extremely unlikely in a vote set for the next few days.

At the same time, Senate leaders from both parties worked on their own fallback measure that would allow Obama to raise the debt limit without a prior vote by lawmakers, discussions that now have expanded to include House officials and top White House aides.

That plan was likely to include limits on spending across thousands of government programs, and possibly a down payment on cuts, as well.

As part of that proposal, a panel of lawmakers would recommend cuts in benefits programs by the end of the year, with the House and Senate required to vote yes-or-no on the package without possibility of changes.

“If they show me a serious plan I’m ready to move,” declared Obama at his second news conference of the week, even though he said he wanted a far more sweeping deal that might even have raised the age of Medicare eligibility from 65 to 67 if Republicans would increase selected taxes.

“We are obviously running out of time,” he said.

Senate Republican leader Mitch McConnell said, “Now the debate will move from a room in the White House to the House and Senate floors,” an indication that the daily closed-door negotiations on Obama’s home ground were a thing of the past.

The House Republican rank and file were advised in a GOP meeting that, barring action by Congress, the government would be able to pay only about half its bills after Aug. 2, and separately that a default could cost the government trillions of dollars in the form of higher interest rates on the debt.

“No matter what 50 percent you choose to pay, there are things in that 50 percent you don’t pay that would have really severe consequences,” Rep. John Campbell, R-Calif., said afterward.

“There are people out there who keep saying we don’t need to increase the debt limit at all. I think this was a way of saying, the people who are saying that need to look at the practical consequences of what they are saying.”

Rep. Paul Ryan, of Wisconsin, chairman of the House Budget Committee, told reporters after the meeting he had discussed the additional costs generated by a default — an event that would be likely to raise interest rates.

At his news conference, Obama said that would mean “effectively a tax increase on everybody” by affecting car purchasers, students and businesses.

The second White House news conference in a week was a testament to the overriding political and economic significance of the issue that has convulsed Congress as well as the administration.

Urging lawmakers to cut trillions from deficits at the same time they raise the debt limit, the president said he favored a balanced approach that included spending cuts, changes to huge government benefit programs and higher taxes on wealthy individuals and certain industries.

It was an offer Republicans could — and did — refuse.

“There are going to be no tax hikes because tax hikes destroy jobs,” said House Speaker John Boehner of Ohio.

While Boehner had earlier shown some flexibility on closing tax loopholes as part of an unprecedented deal with Obama, many Republican lawmakers are adamant that deficit reductions be limited to spending cuts.

To underscore their conservative priorities, GOP leaders scheduled a vote for next week on legislation they said would cut $111 billion in the budget year that begins Oct. 1. It would also require a steady decline in spending as a percentage of the overall economy over the next decade.

Even some supporters conceded it was a symbolic gesture given the realities of divided government.

“I think everybody knows the president won’t sign this,” Campbell said after the closed-door Republican meeting.

“But we’re putting a marker down, and that’s an important step that begins the process of resolving this,” he added.

If so, it was in a style that only congressional insiders might recognize as the beginning of the endgame to an unprecedented problem.

McConnell issued a statement announcing the Senate would vote on both a balanced budget amendment and the House’s “Cut, Cap and Balance Plan.”

His statement didn’t say so, but neither measure has much, if any, chance of passage in the Democratic-controlled Senate.

Still, the votes themselves would clear the way for debate on the fallback plan the two Senate leaders have been working on for the past several days.

Senate aides said the measure was not yet fully drafted, but likely to come up for debate by the end of next week.

Obama offered measured praise for that option: “It is constructive to say that if Washington operates as usual and can’t get something done, let’s at least avert Armageddon.”

A two-thirds vote of each house is required for passage of a constitutional amendment. Approval would send the issue to the states, where ratification by three quarters of the legislatures is needed to make it part of the Constitution.

Presidents play no official role in amending the Constitution, but Obama expressed his opposition to the GOP-backed measure anyway.

“We don’t need a constitutional amendment to do that. What we need to do is do our jobs,” he said.