WASHINGTON — Ending a perilous stalemate, President Barack Obama and congressional leaders announced historic agreement Sunday night on emergency legislation to avert the nation’s first-ever financial default.

The dramatic resolution lifted a cloud that had threatened the still-fragile economic recovery at home — and it instantly powered a rise in financial markets overseas.

The agreement would slice at least $2.4 trillion from federal spending over a decade, a steep price for many Democrats, too little for many Republicans. The Treasury’s authority to borrow would be extended beyond the 2012 elections, a key objective for Obama, though the president had to give up his insistence on raising taxes on wealthy Americans to reduce deficits.

The deal, with scant time remaining before Tuesday’s debt-limit deadline for paying government bills, “will allow us to avoid default and end the crisis that Washington imposed on the rest of America,” the president said in an announcement at the White House.

Default “would have had a devastating effect on our economy,” he said.

House Speaker John Boehner telephoned Obama at mid-evening to say the agreement had been struck, then immediately began pitching the deal to his fractious rank and file.

“It isn’t the greatest deal in the world, but it shows how much we’ve changed the terms of the debate in this town,” he said on a conference call, according to GOP officials. He added the agreement was “all spending cuts. The White House bid to raise taxes has been shut down.”

Rep. Nancy Pelosi, was non-committal. “I look forward to reviewing the legislation with my caucus to see what level of support we can provide,” she said in a written statement.

No votes were scheduled in either house of Congress before Monday, to give rank and file lawmakers time to review the package. Senate approval seems virtually certain; the House could prove more difficult.

Without legislation in place by Tuesday, the Treasury would not be able to pay all its bills, raising the threat of a default that administration officials say could do catastrophic damage to the economy.

If approved, though, a compromise would presumably preserve America’s sterling credit rating, reassure investors in financial markets across the globe and possibly reverse the losses that spread across Wall Street in recent days as the threat of a default grew.

Even word of an impending deal earlier in the day by Senate Republican Leader Mitch McConnell of Kentucky sent U.S. stock futures upward. And before Obama had finished speaking, Japan’s benchmark Nikkei index, opening Monday morning — at 8 p.m. Sunday on America’s East Coast — was up 1.7 percent in early trading.

Pending final passage, the agreement marked a dramatic reach across party lines that played out over six months and several rounds of negotiating, interspersed by periods of intense partisanship.

Vice President Joe Biden, who played an important part in this weekend’s negotiations, agreed. He tweeted: “Compromise makes a comeback.”

Not everyone felt that way.

“Someone has to say no. I will,” said Rep. Michele Bachmann, R-Minn., a contender for the 2012 Republican presidential nomination.