Congress approved a plan to end Washington’s long drama over the “fiscal cliff” late Tuesday after House Republicans surrendered to President Obama’s demand to let taxes rise on the nation’s richest households.

The House voted 257 to 167 to send the measure to Obama for his signature; the vote came less than 24 hours after the Senate overwhelmingly approved the legislation.

House Speaker John A. Boehner (Ohio) and most other top GOP leaders took no public position on the measure and offered no public comment before the 10:45 p.m. vote. Boehner declined even to deliver his usual closing argument, leaving House Ways and Means Committee Chairman Dave Camp (R-Mich.) to defend the measure as the “largest tax cut in American history.”

The bill will indeed shield millions of middle-class taxpayers from tax increases set to take effect this month. But it also will let rates rise on wages and investment profits for households pulling in more than $450,000 a year, marking the first time in more than two decades that a broad tax increase has been approved with GOP support.

The measure also will keep benefits flowing to 2 million unemployed workers on the verge of losing their federal checks. And it will delay for two months automatic cuts to the Pentagon and other agencies that had been set to take effect Wednesday.

The impact of tax increases on taxpayers

Many economists had warned that the scheduled tax increases and spending cuts would have plunged the economy back into recession.

Conservatives complained bitterly that the legislation would raise taxes without making any significant cuts in government spending. For much of the day, the measure appeared headed for defeat as Boehner contemplated tacking on billions in spending cuts, a move that would have derailed a compromise that the White House and Senate leaders had carefully crafted.

In the end, GOP lawmakers decided not to take a gamble that could force the nation to face historic tax increases for virtually every American — and leave House Republicans to take the blame.

“I don’t know if playing chicken with the American people at this point is in the best interest of the people,” said freshman Rep. Lou Barletta (R-Pa.).

The bill drew 85 votes from Republicans and 172 from Democrats, meaning well more than half of its support came from the Democratic minority.

With 151 Republicans voting “no,” the GOP tally fell far short of a majority of the GOP caucus. That broke a long-standing preference by Boehner to advance only bills that could draw the support of a majority of his Republican members.

In a sign of the moment’s gravity, Boehner himself cast a rare vote: He supported the bill. So did Rep. Paul Ryan (Wis.), the GOP’s vice-presidential candidate last year, who parted ways from Sen. Marco Rubio (R-Fla.), a potential 2016 presidential contender, who voted against the measure.

But other top GOP leaders voted no, including Majority Leader Eric Cantor (Va.) and Majority Whip Kevin McCarthy (Calif.).

Boehner was humiliated just two weeks ago when the Republican rank-and-file refused to support a GOP alternative that would have permitted taxes to rise only on income over $1 million a year. But when he scheduled a vote on the Senate bill, even some of the chamber’s staunchest conservatives agreed that giving up the fight was probably the best course.

In a brief statement, Obama praised congressional leaders for advancing the legislation, which he said would produce $620 billion in new tax revenue. “But I think we all recognize this law is just one step in the broader effort to strengthen our economy and broaden opportunity for everybody,” he said, noting that the fight over the budget will continue when the new Congress faces the imposition of sequestration cuts in just two months.

But Obama warned again that he would not negotiate with Republicans over the $16.4 trillion debt limit, which must be raised in the coming weeks. “While I will negotiate over many things,” he said, “I will not have another debate with this Congress over whether they will pay the bills they’ve already racked up.”

With that, Obama took off for Hawaii, where he left his wife and daughters the day after Christmas. It was unclear when he planned to sign the fiscal cliff measure, which calls for the top tax rate to rise immediately from 35 percent to 39.6 percent on income over $450,000 for married couples and $400,000 for single people.

The measure will protect more than 100 million families earning less than $250,000 a year from significant income tax increases set to take effect this month — although their payroll taxes will rise with the expiration of a temporary tax cut adopted two years ago.

In addition to avoiding much of the fiscal cliff, the measure will extend federal dairy policies through September, averting a threatened doubling of milk prices. The measure also will cancel a scheduled pay raise for members of Congress.

After weeks of partisan bickering over whether taxes should increase for anyone, the compromise bill rolled through the Senate early Tuesday in a highly unusual New Year’s Day vote. The vote was 89 to 8, with both parties offering overwhelming support.

The moment served as a rare bipartisan coda to what has been one of the most rancorous, partisan Congresses in recent history. The 11 senators who are retiring received hugs and kisses from their colleagues. The current Congress ends at noon Thursday, when the new Congress will be seated, and lawmakers would have been forced to scrap the fiscal-cliff legislation and start over.

Three Democrats voted against the measure, including liberal Tom Harkin (Iowa), and moderates Thomas R. Carper (Del.) and Michael F. Bennet (Colo.).

Bennet complained that the bill would do little to reduce record budget deficits. According to the nonpartisan Congressional Budget Office, the measure would cause the national debt to be $4 trillion higher by 2022 than if all of the cliff’s tax increases and spending cuts had been allowed to take effect.

Five Senate Republicans also rejected the measure, including tea party favorites Rand Paul (Ky.) and Mike Lee (Utah).

But 40 others voted for it, including such GOP leaders on tax-and-spending policy as Sen. Patrick J. Toomey (Pa.) and Ronald H. Johnson (Wis.), a tea party star who frequently consults with House conservatives.

Neither party was entirely happy with the bill. While conservatives complained about new taxes and a lack of spending reductions, liberals complained about its provisions regarding inherited estates.

Although the tax rate will rise from 35 percent to 40 percent, estates worth as much as $5 million — $10 million for married couples — will go untaxed. And an inflation adjustment will guarantee that the size of the exemption will grow to $15 million for couples by the end of the decade.

Still, House Democrats largely embraced the measure, which was negotiated by Vice President Biden and Senate Minority Leader Mitch McConnell (R-Ky.) and endorsed by Obama. After receiving a point-by-point 90-minute briefing from Biden on Tuesday, Democrats rallied around the package.

“It’s long overdue for us to have this solution to go forward and remove all doubt as to what comes next for our country,” said House Minority Leader Nancy Pelosi (D-Calif.).

But it was a different story among House Republicans, who at first appeared to strongly oppose it. In the early afternoon, the GOP gathered for the first of two lengthy closed-door briefings in the basement of the Capitol.

There, Boehner told members that he wanted to hear their views but would not take a position. Cantor, meanwhile, “forcefully” aired concerns that the measure would raise taxes but not cut spending, said Rep. Jeff Flake (R-Ariz.). Afterward, Cantor emerged and told reporters: “I do not support the bill.”

That view was widespread in the room, where House members vented their frustrations at the Senate for foisting the arrangement upon them. Many rose to say they should take advantage of the legislative process, tack on billions in new spending reductions and force the Senate to respond.

“We should not take a package put together by a bunch of sleep-deprived octogenarians on New Year’s Eve,” retiring Rep. Steven C. LaTourette (R-Ohio) said in a dig at Senate leaders. LaTourette, who has championed ambitious deficit-reduction efforts, faced the prospect of casting his last vote in Congress for a measure that would sharply deepen deficits.

Rep. Spencer Bachus (R-Ala.) said a consensus was developing that the GOP should amend the Senate’s plan. “I would be shocked if the bill did not go back to the Senate,” he said.

The negative reaction threatened to plunge Washington back into the high-stakes, last-minute drama that has characterized both the fiscal-cliff negotiations and a series of other recent confrontations between the two parties over spending and taxes, including the fight over raising the federal borrowing limit in the summer of 2011.

Senate Democrats and administration officials warned that the Senate would reject any move to amend the measure. The House would be responsible for a dive over the cliff hours before U.S. financial markets were set to open Wednesday after the New Year’s holiday.

For hours, there was no decision on how to proceed. As leaders huddled, rank-and-file members returned to their offices and were greeted with confusing messages from conservatives and constituents.

Former House speaker Newt Gingrich (R-Ga.), who has opposed any deal to raise taxes, voiced support for Cantor. But conservative writer William Kristol, wrote a blog post titled “Say Yes to the Mess.”

“Politically, Republicans are escaping with a better outcome than they might have expected, and President Obama has gotten relatively little at his moment of greatest strength,” Kristol said, advising House Republicans to take the deal.

Shortly before dinner, Republicans gathered behind closed doors again to settle on a new plan: Leaders would survey members about the spending-cut package to determine if it could pass. If not, they would allow the Senate bill to move ahead.

Around 8 p.m., they announced a decision. The Senate bill would receive a vote, with the expectation that Democrats and Republicans would join forces to approve the measure.

During floor debate, Camp, chairman of the tax-writing Ways and Means Committee, said GOP members should support the bill because it would make “permanent tax policies Republicans originally crafted” under President George W. Bush.

Rep. Sander M. Levin (Mich.), the ranking Democrat on the Ways and Means Committee, countered that Democrats should back the bill because it would let the Bush tax cuts expire for the wealthy, breaking the “iron barrier” to tax increases since 1993.

Paul Kane and Ed O’Keefe contributed to this report.