After a rare holiday session that lasted through the New Year’s Eve celebration and two hours into New Year’s Day, the Senate voted, 89-8, to approve the proposal. Republican leaders in the House had balked at holding a vote in the dark of night, but are expected to bring the bill up later Tuesday.

The House, where GOP lawmakers have been resistant to voting for a tax increase, will now determine whether the nation’s plunge off the fiscal cliff is halted. As long as Congress is seen to be working toward a solution, no dire economic fallout is expected from the delay.

The deal would represent a milestone for Republicans, whose anti-tax stance has defined the party since former President George H.W. Bush in 1990 broke his promise not to raise taxes. Republicans have not supported an effort to increase income taxes since then.

It also would be a concession for Democrats who backed away from President Barack Obama’s popular campaign pledge that he would ask households earning more than $250,000 to pay more in taxes. Under the deal with Republicans, taxes will increase only on households earning more than $450,000.

The deep automatic spending cuts scheduled to begin Wednesday — the other part of the “fiscal cliff” — would be pushed back just long enough to ensure that the partisan budget battles marking Obama’s first term will also punctuate the beginning of his second. Negotiations over the cuts were expected to be rolled into talks about extending the nation’s debt ceiling, a prospect Democrats promised to resist.

The normally festive time of year turned serious Monday as details emerged of the deal. Vice President Joe Biden, who brokered the deal in marathon sessions with Mitch McConnell, the Senate’s Republican minority leader, was dispatched to the Capitol for an intense 90-minute session with Democrats.

In an afternoon speech with middle-class Americans arrayed on risers behind him, Obama had urged congressional negotiators to press on and resolve the remaining issues.

“It’s not done,” Obama said from the Eisenhower Executive Office Building next to the White House. He called on Americans to urge their lawmakers to “see if we can get this done.”

The talks had largely settled the income tax provisions, which would stop the increase on most Americans and raise rates for households making more than $450,000 a year. But the two sides remained at odds over how to deal with the automatic spending cuts.

“We are very, very close,” an upbeat McConnell said on the Senate floor. “We can do this.”

Lawmakers were told to stay near the Capitol, and many hunkered down there for New Year’s Eve.

Sen. Mary L. Landrieu, D-La., hosted an evening gathering at her nearby home as lawmakers awaited word of final details. “We’re serving beer, not champagne,” she said.

Yet Democratic leaders remained largely silent on the proposal before Biden, a former senator who has cut deals with McConnell before, headed to Capitol Hill to brief his Democratic colleagues.

“Having been in the Senate as long as I have, there are two things you shouldn’t do: You shouldn’t predict how the Senate’s going to vote before they vote,” Biden said, emerging from the session, which lawmakers described as “robust.” “And No. 2, you surely shouldn’t predict how the House is going to vote.”

The office of Senate Majority Leader Harry Reid, the Nevada deal-maker who stepped aside for Biden to negotiate with McConnell, offered visible evidence of the level of concern. Lawmakers came in and out of his door throughout the day.

“No deal is better than a bad deal,” said Sen. Tom Harkin, D-Iowa, an influential liberal. “And this looks like a very bad deal.”

The powerful AFL-CIO president, Richard Trumka, tweeted his displeasure.

Conservatives similarly sounded off. “Republicans should kill the compromise, if there are no spending cuts,” Erick Erickson, the conservative founder of the influential Red State blog, said in a tweet.

Putting the vote off until Tuesday would accomplish a political back flip that would be particularly advantageous for anti-tax Republicans, and it represented an option that has been discussed for months.

With the existing tax rates set to expire at midnight, Tuesday ushered in the new higher rates. By acting Tuesday, rather than Monday, the congressional votes would be to lower tax rates on most Americans, rather than raise them.

Biden and McConnell were in close contact all day after working past midnight Sunday and resuming very early Monday morning to craft the deal.

The minority leader convened Republican senators behind closed doors at dinnertime, and many emerged optimistic that a deal was at hand.

“Hope springs eternal around here, even though it gets a little sticky at times,” said Sen. Pat Roberts, R-Kan. House Speaker John Boehner, R-Ohio, similarly convened his troops in a basement office beneath the Rotunda.

Optimism aside, one thing was increasingly clear: With some major issues still unresolved, Washington was poised to continue the partisan budget battles that have defined Obama’s first term.

Under the proposed deal, more than $620 billion in revenue would be raised — far less than the $1.6 trillion Obama first sought in new revenue when he still hoped for a large deficit-reduction package.

The agreement would set the top tax rates at 39.6 percent for income above $450,000 for households and $400,000 for individuals, according to a source who spoke on the condition of anonymity because he was not authorized to discuss the negotiations.

Tax rates on investment income would also rise for those higher-income households, from the historic low 15 percent rate on capital gains and dividends to 20 percent. Obama had wanted to tax dividends at the same rate as ordinary income.

The rate for the estate tax was a key sticking point throughout the weekend. The agreement would set a new rate at 40 percent on estates valued at more than $5 million. That is a compromise between the 35 percent rate in effect last year and the 45 percent rate Democrats demanded on estates of $3.5 million or more.

About 2 million out-of-work Americans would benefit, if the deal is approved, from a one-year extension of long-term unemployment benefits. Those benefits expired over the weekend.

One area that hewed closer to Democratic priorities was Obama’s proposal to reinstate limits on how much upper-income households could benefit from personal exemption tax credits and itemized deductions. Those limits, in place before the George W. Bush-era tax cuts began in 2001, were done away with over the past decade.

The agreement would reduce those deductions for households earning more than $250,000, leading to higher effective taxes on those households without an increase in tax rates, which Republicans had resisted.

Other tax credits established under Obama’s economic recovery program would also be extended for five more years. That provision is a nod to Democratic calls for more stimulus spending to help the economy and for adjustments to the tax code to help those with more modest incomes.

Those credits include a $2,500 tax credit for college students and another that allows cash refunds even if no tax is owed for those with children and family incomes below $45,000.

The deal also includes a permanent fix for the alternative minimum tax, a part of the tax code that was established decades ago to ensure high-income earners paid at least a minimum amount of tax even if they were able to reduce their liability through extensive deductions. But it increasingly snares middle-class families because it was never indexed to inflation. Congress must fix it every year, a problem that would be finally resolved with Monday’s deal.

The agreement also includes a nine-month extension of a stalled farm bill, ensuring that milk prices would not double, as some had predicted, without price supports. Doctors who serve Medicare patients would also be spared a pay cut, a usually routine adjustment that got caught up in the year-end fight.

Even with the thorny tax issues all but settled, the mandatory budget cuts that would start to reduce federal spending on Wednesday remained a sticking point until late Monday.

Those cuts, which would slice across defense and domestic programs, had been set as a last-ditch trigger designed to spur negotiations for a broader budget deal after an earlier deficit-reduction effort failed.

Talks focused on postponing the cuts for two months but offsetting the $24 billion that would not be saved. The White House and Republicans eventually settled on a mix of revenue increases and spending cuts.

Postponing the automatic cuts for two months, as the Republicans wanted, all but guarantees the budget battles will continue. Democrats had hoped to extend that reckoning for a year to keep Obama’s second term from beginning with a repeat of past tumultuous budget battles.