A plan to suspend the federal debt limit cleared a key hurdle in the House on Wednesday, easing the threat of a government default for at least four months.

But congressional leaders were already looking toward the next crisis: deep automatic spending cuts that look increasingly likely to hit the Pentagon and other federal agencies on March 1.

Leaders in both parties predicted Wednesday that the cuts, known as sequestration, will take effect at least briefly while policymakers try to restart talks over a far-reaching plan to lower the national debt.

“It’s going to happen,” said Sen. Richard J. Durbin (Ill.), the No. 2 Democrat in the Senate, noting that Republicans in both chambers are determined to let the cuts take effect, saving $1.2 trillion over the next decade.

“I think we are committed to some form of sequestration spending cut,” Durbin said, adding that the White House is “talking about some options” for blunting the impact on government services and federal workers.

After the sequester comes the threat of a government shutdown on March 27. And after that, probably sometime this summer, the threat of default will once again loom unless lawmakers can reach a consensus on long-term tax and spending policies.

Senate Democratic leaders argued that House Republicans are likely to capitulate again on raising the debt limit and that Wednesday’s vote suggests they have lost the taste for confrontation that has driven the nation repeatedly to the brink of fiscal crisis over the past two years.

“This sets a new precedent that the debt limit will not be taken hostage going forward,” said Sen. Charles E. Schumer (D-N.Y.).

But even as House Republicans voted to suspend enforcement of the debt ceiling through May 18, their budget chairman vowed to use the coming deadlines to force President Obama and Senate Democrats to deliver “a big down payment on the debt crisis.”

“Spending cuts are coming,” House Budget Committee Chairman Paul Ryan (Wis.) told reporters at a breakfast hosted by the Wall Street Journal. “We are not going to lose the $1.2 trillion we’ve already got from the last debt-ceiling [fight]. We are going to have to negotiate on top of that for a new debt-ceiling increase. . . . We’re very serious about this.”

He and other House leaders rallied GOP support for Wednesday’s debt-limit vote by promising to deliver a budget plan that would wipe out deficits within the next decade — a daunting task. For the past two years, the House has passed budgets that propose to cut spending far more deeply than Obama and other Democrats are willing to accept, and even those austere frameworks would take nearly 30 years to achieve balance.

Meanwhile, Ryan ruled out the possibility of lowering deficits by raising taxes, as Democrats prefer. The “fiscal cliff” deal approved this month would generate about $650 billion in new tax revenue over the next decade. That, Ryan said, is enough.

“They got their revenue increases already,” he said.

Ryan’s hard-line position on the budget appeared to reassure House Republicans, who voted overwhelmingly for Wednesday’s debt-limit measure. It passed on a vote of 285 to 144, with 33 Republicans voting no.

More than half of House Democrats voted against the legislation, arguing that a longer extension of the debt limit is necessary to bring certainty to the sluggish economy. But Democrats delivered enough votes to push the measure across the finish line, giving Speaker John A. Boehner (R-Ohio) a badly needed victory after a series of embarrassing revolts from conservative members of his party.

Among those voting with Boehner were Reps. Steve Stockman (R-Tex.) and Mick Mulvaney (R-S.C.), who just three weeks ago refused to support Boehner in the formal vote for House speaker. Later, after the measure easily amassed enough votes to pass, Stockman joined some other conservatives in switching his vote to “no” — a sign that he opposed the measure but was willing to support Boehner if his vote had been needed.

Under the proposal, the Treasury Department would be permitted to ignore the $16.4 trillion cap on government borrowing, running up additional debt to pay the nation’s bills through May 18. At that point, the debt limit would automatically reset at a higher level.

In an analysis released Wednesday, the Bipartisan Policy Center predicted that the Treasury would run up about $450 billion in additional debt during that period and that the date of potential default would be postponed at least until the end of July.

The House measure also requires senators to adopt their own budget blueprint by April 15 or have their paychecks withheld and placed in escrow until this session of Congress ends in 2015.

“The premise here is pretty simple,” Boehner said during the House debate. “It says that there should be no long-term increase in the debt limit until there’s a long-term plan to deal with the fiscal crisis that faces our country.”

Boehner said the House would not agree in May to a long-term increase in the debt ceiling without a deal that would significantly reduce deficits. “It’s time for Congress to get serious about this,” he said.

Just before the vote, Democratic leaders in the Senate said they would accept the House debt-limit measure without changes; a Senate vote is expected as soon as next week. The White House, too, has said Obama would not stand in the way of the bill.

Meanwhile, the president is due to submit his budget request to Congress sometime next month. Senate Budget Committee Chairman Patty Murray (D-Wash.) said Wednesday that the Senate would also adopt a budget blueprint this year, marking the first time Senate Democrats have undertaken that task since 2009.

“Democrats are eager to contrast our pro-growth, pro-middle class budget priorities with the House Republicans’ Ryan budget that would end Medicare as we know it, gut investments in jobs and programs middle class families depend on, and cut taxes for the wealthiest Americans and biggest corporations,” Murray said in a statement. “We know that when our priorities are laid out next to Republicans’, the public stands with us.”

Paul Kane contributed to this report.