President Obama on Tuesday hailed an ambitious new deficit-reduction plan that is gaining momentum in the Senate, calling it a “very significant step” and saying it could provide the vehicle to break an impasse over raising the federal borrowing limit while cutting the nation’s debt.

Appearing at the regular White House news briefing, Obama said the bipartisan proposal is “broadly consistent” with the approach he has advocated, in that it reduces discretionary spending and tackles health-care spending and entitlements while also raising additional revenue.

But in the event that an agreement capable of passing Congress is not reached before a looming deadline to raise the federal debt ceiling, Obama said, lawmakers should finishing hammering out a backup plan now being negotiated by the Senate’s Democratic and Republican leaders.

“The problem we have now is we’re in the 11th hour, and we don’t have a lot more time left,” Obama said. “We don’t have any more time to engage in symbolic gestures. We don’t have any more time to posture.” He was referring to a House Republican plan, called the “Cut, Cap and Balance Act,” which aims to slash federal spending, impose a cap on future outlays and amend the Constitution to require a balanced budget — without increasing revenue. “That is not an approach that could pass both chambers, it’s not an approach that I would sign, and it’s not balanced,” Obama said.

Obama spoke after more than 40 Republicans and Democrats attended a morning briefing on the new Senate proposal, which would slice $3.7 trillion from the federal budget over the next decade.

The plan, drafted by a bipartisan group of senators known as the “Gang of Six,” has been in the works for months. After struggling to reach consensus and apparently disbanding last week, the group now says it’s nearing agreement on a proposal, which could offer an alternative strategy for pushing an increase in the debt limit through Congress before an Aug. 2 deadline.

“We’ve gone from a Gang of Six to a mob of 50,” exulted Sen. Joe Manchin (D-W. Va.), as he emerged from the meeting. The proposal, Manchin said, “shows great promise.”

“I will support it. It is a fair compromise,” added Sen. Kay Bailey Hutchison (R-Tex.). “This is a way forward where we can do the work that we have come here to do.”

Obama called the plan “good news.” He told reporters: “What it says is we’ve got to be serious about reducing discretionary spending both in domestic spending and defense; we’ve got to be serious about tackling health care spending and entitlements in a serious way; and we’ve got to have some additional revenue so that we have an approach in which there is shared sacrifice and everybody is giving up something.”

He said he would urge Senate and House leaders of both parties to be “prepared to start talking turkey” on Wednesday and craft a plan that can meet the Aug. 2 deadline.

Details of the plan were sketchy, and it was not immediately clear how the proposal might be combined with existing debt-limit strategies. As described by its creators, the framework calls for $500 billion in immediate spending cuts as a downpayment on a broader debt-reduction effort that would be carried out largely by existing legislative committees.

Those committees would be given targets for savings from overhauling entitlement programs and rewriting the tax code. If the committees failed to produce a plan to meet the targets over the next six months, 10 senators — five from each party — could step in to offer their own debt-reduction plan.

The overall goals of the plan mirror President Obama’s fiscal commission: Deep cuts in government agencies, significant reductions in Medicare and a framework for keeping Social Security solvent over the next 75 years. It also seeks to raise $1 trillion in taxes over the next decade by rewriting the tax code to lower tax rates for households in all income categories while eliminating various tax breaks and deductions.

Republicans and Democrats alike welcomed the plan. And while several said it would be difficult to bring it before the Senate before Aug. 2, they said it could provide a good alternative to the 12-member special committee proposed by Senate Majority Leader Harry M. Reid (D-Nev.), which many fiscal hawks were coming to view as a likely dead end in the debt-reduction process.

“This is a good foundation for debate,” said Sen. Johnny Isakson (R-Ga.), as he left the meeting in an out-of-the-way conference room near the entrance to the Capitol. “They ought to get it to the point where it’s debatable by every member of the Senate, and not in a corner somewhere.”

Four of the original members of the Gang of Six — Democrats Mark Warner (Va.) and Kent Conrad (N.D.) and Republicans Saxby Chambliss (Ga.) and Mike Crapo (Idaho) — said the next step is to receive feedback from their colleagues and see whether they can get a filibuster-proof majority of 60 to sign on. Then they will decide how to move forward.

“This was always a debt-reduction exercise, not an extension-of-the-debt-limit exercise,” said Conrad, who chairs the Senate Budget Committee. “How those two come together or don’t, I don’t know the answer to that yet.”

The Gang of Six formed in the wake of Obama’s fiscal commission, an 18-member panel whose ideas sparked widespread interest but failed to win the needed 14 votes to send its recommendations to the floor of the House and Senate. Reluctant to let the effort fade away, commission members Conrad and Crapo joined forces with Warner and Chambliss to try to draft the commission plan into a legislation.

The Gang of Six stumbled after two other members — Sen. Richard J. Durbin (D-Ill.) and Sen. Tom Coburn (R-Okla.) — reached an impasse over cuts to entitlement programs and Coburn left the group in mid-May. A last-ditch effort to reach agreement last week failed, and members said the group had disbanded.

“We have a plan. We need a gang,” Durbin told reporters with evident frustration.

But on Tuesday, Coburn was back, saying the plan had been tweaked to add more than $100 billion in cuts to health care programs.

“The plan has moved significantly, and it’s where we need to be,” he told reporters. “This creates the way forward to where we can solve our problems.”

The development comes as lawmakers and the Obama administration are struggling to develop a debt-reduction plan that would persuade a hostile Congress to raise the legal limit on government borrowing. Unless Congress acts to lift the $14.3 trillion debt limit by Aug. 2, Treasury officials have said the government will begin to default on its obligations.

The House was moving forward Tuesday with a separate proposal to cap government spending and make raising the debt limit contingent upon congressional passage of a balanced budget amendment to the U.S. constitution. With that plan given almost no chance of approval in the Senate — and with Obama threatening to veto it — House Speaker John A. Boehner (R-Ohio) conceded that quiet conversations are underway regarding alternatives.

“I’m not giving up on cut, cap and balance,” Boehner said. “But I do think it’s responsible for us to look at what Plan B would look like.”

Staff writer Rosalind S. Helderman contributed to this report.