WASHINGTON — Past its own New Year’s deadline, a weary Congress sent President Barack Obama legislation to avoid a national “fiscal cliff” of middle class tax increases and spending cuts late Tuesday night in the culmination of a struggle that strained America’s divided government to the limit.

The bill’s passage on a 257-167 vote in the House sealed a hard-won political triumph for the president less than two months after he secured re-election while calling for higher taxes on the wealthy.

In addition to neutralizing middle class tax increases and spending cuts taking effect with the new year, the legislation will raise tax rates on incomes over $400,000 for individuals and $450,000 for couples. That was higher than the thresholds of $200,000 and $250,000 that Obama campaigned for. But remarkably, in a party that swore off tax increases two decades ago, dozens of Republicans supported the bill at both ends of the Capitol.

The Senate approved the measure on a vote of 89-8 less than 24 hours earlier, and in the interim, rebellious House conservatives demanded a vote to add significant spending cuts to the measure. But in the end they retreated.

Supporters of the bill in both parties expressed regret that it was narrowly drawn, and fell far short of a sweeping plan that combined tax changes and spending cuts to reduce federal deficits. That proved to be a step too far in the two months since Obama called congressional leaders to the White House for a postelection stab at compromise.

Majority Republicans did their best to minimize the bill’s tax increases, just as they abandoned their demand from earlier in the day to add spending cuts to the package.

“By making Republican tax cuts permanent, we are one step closer to comprehensive tax reform that will help strengthen our economy and create more and higher paychecks for American workers,” said Rep. Dave Camp of Michigan, chairman of the tax-writing House Ways and Means Committee.

He urged a vote for passage to “get us one step closer to tax reform in 2013” as well as attempts to control spending.

House Democratic Leader Nancy Pelosi also said the legislation included “permanent tax relief for the middle class,” and she summoned lawmakers to provide bipartisan support as the Senate did.

The bill would also prevent an expiration of extended unemployment benefits for an estimated two million jobless, block a 27 percent cut in fees for doctors who treat Medicare patients, stop a $900 pay increase for lawmakers from taking effect in March and head off a threatened spike in milk prices.

It would stop $24 billion in across-the-board spending cuts set to take effect over the next two months, although only about half of that total would be offset with savings elsewhere in the budget.

The economic as well as political stakes were considerable.

Economists have warned that without action by Congress, the tax increases and spending cuts that technically took effect with the turn of the new year at midnight could send the economy into recession.

Even with enactment of the legislation, taxes are on the rise for millions.

A 2 percentage point temporary cut in the Social Security payroll tax, originally enacted two years ago to stimulate the economy, expired with the end of 2012. Neither Obama nor Republicans made a significant effort to extend it.

House Republicans spent much of the day struggling to escape a political corner they found themselves in.

“I personally hate it,” Rep. John Campbell of California, said of the measure, giving voice to the concern of many Republicans that it did little or nothing to cut spending.

“The speaker the day after the election said we would give on taxes and we have. But we wanted spending cuts. This bill has spending increases. Are you kidding me? So we get tax increases and spending increases? Come on.”

House Majority Leader Eric Cantor told reporters at one point, “I do not support the bill. We are looking, though, for the best path forward.”

Within hours, Republicans abandoned demands for changes and agreed to a simple yes-or-no vote on the Senate-passed bill.

They feared that otherwise the Senate would refuse to consider any alterations, sending the bill into limbo and saddling Republicans with the blame for a whopping middle class tax increase. One Senate Democratic leadership aide said Majority Leader Harry Reid would “absolutely not take up the bill” if the House changed it. The aide spoke on condition of anonymity, citing a requirement to keep internal deliberations private.

Despite Cantor’s remarks, Speaker John Boehner took no public position on the bill as he sought to negotiate a conclusion to the final crisis of a two-year term full of them.

The brief insurrection wasn’t the first time that the tea party-infused House Republican majority has rebelled against the party establishment since the GOP took control of the chamber 24 months ago. But with the two-year term set to end Thursday at noon, it was likely the last. And as was true in earlier cases of a threatened default and government shutdown, the brinkmanship came on a matter of economic urgency, leaving the party open to a public backlash if tax increases do take effect on tens of millions.

The non-partisan Congressional Budget Office said the measure would add nearly $4 trillion over a decade to federal deficits, a calculation that assumed taxes would otherwise have risen on taxpayers at all income levels. There was little or no evident concern among Republicans on that point, presumably because of their belief that tax cuts pay for themselves by expanding economic growth and do not cause deficits to rise.

The relative paucity of spending cuts was a sticking point with many House Republicans. Among other items, the extension of unemployment benefits costs $30 billion, and is not offset by savings elsewhere.

Others said unhappiness over spending outweighed fears that the financial markets will plunge on Wednesday if the fiscal cliff hasn’t been averted.

“There’s a concern about the markets, but there’s a bigger concern, which is getting this right, which is something we haven’t been very good at over the past two years,” said Rep. Steve LaTourette of Ohio.

For all the struggle involved in the legislation, even its passage would merely clear the way for another round of controversy almost as soon as the new Congress convenes.

With the Treasury expected to need an expansion in borrowing authority by early spring, and funding authority for most government programs set to expire in late March, Republicans have made it clear they intend to use those events as leverage with the administration to win savings from Medicare and other government benefit programs.

McConnell said as much moments before the 2 a.m. Tuesday vote in the Senate — two hours after the advertised “cliff” deadline.

“We’ve taken care of the revenue side of this debate. Now it’s time to get serious about reducing Washington’s out-of-control spending,” he said. “That’s a debate the American people want. It’s the debate we’ll have next. And it’s a debate Republicans are ready for.”

The 89-8 vote in the Senate was unexpectedly lopsided.

Despite grumbling from liberals that Obama had given way too much in the bargaining, only three Democrats opposed the measure.

Among the Republican supporters were Sen. Pat Toomey of Pennsylvania, an ardent opponent of tax increases, as well as Sen. Ron Johnson of Wisconsin, elected to his seat two years ago with tea party support.