The Senate on Wednesday approved the $858 billion tax plan negotiated by the White House and Republican leaders, and House Democrats said they expected to pass the bill Thursday.

WASHINGTON — The Senate on Wednesday approved the $858 billion tax plan negotiated by the White House and Republican leaders, and House Democrats said they expected to pass the bill Thursday after a final, seemingly futile effort to change a provision that benefits wealthy estates.

The Senate vote was 81-19 as Democrats yielded in their long push to end the Bush-era tax rates for high-income taxpayers. Republicans agreed to back a huge stimulus package, including an extension of jobless benefits for the long-term unemployed and a one-year Social Security payroll-tax cut for most workers, with the entire cost added to the deficit.

House Democratic leaders said they would bring the bill to the floor Thursday along with an amendment to tax more estates at a higher rate. Democrats privately predicted the amendment would be rejected and the package approved, but House Speaker Nancy Pelosi was not ready to concede.

“We will make our point,” she said at a news conference Wednesday night, repeating her opposition, shared by many Democrats, to the provision granting a tax exemption to estates of up to $5 million per person, or $10 million per couple.

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While many Democrats said the money used to continue reduced tax rates on the highest incomes could be better spent on other steps to stimulate the economy, they made clear their initial fury at the prospect of extending those rates had given way to acceptance that the White House, its leverage weakened by election losses, had negotiated the best compromise it could.

Some Republicans have complained about the price tag of the overall package, but GOP leaders have said they will not accept any change. President Obama also urged Congress to pass the bill unchanged and without delay.

The Senate’s overwhelming approval of the plan was a brief flash of bipartisan cooperation amid the deep partisan acrimony in the waning days of the 111th Congress. The plan was supported by 43 Democrats, including Washington state Sens. Patty Murray and Maria Cantwell, along with 37 Republicans and Sen. Joe Lieberman, I-Conn. Opposed were 13 Democrats, five Republicans and Sen. Bernie Sanders, I-Vt. Lieberman and Sanders caucus with Democrats.

“A tremendous accomplishment,” Senate Majority Leader Harry Reid of Nevada declared shortly before the vote Wednesday. “Whether you agree with all the contents of the bill or not, everyone should understand this is one of the major accomplishments of any Congress where two parties, ideologically divided, have agreed on a major issue for the American people.”

The two-year measure will touch virtually every American — poor and rich, old and young, married or single, with children or living alone, and even those who die. With a reprise of the contentious debate scheduled for the height of the 2012 presidential campaign, the bill is likely to be a precursor to a broader effort by Obama to overhaul the tax code and begin tackling the long-term deficit.

The plan would extend all lowered income-tax rates enacted under President George W. Bush, as well as the 15 percent rate on capital gains and dividends, set to expire this month. And it would set new estate-tax parameters, including the exemptions and a maximum rate of 35 percent. These provisions would last for two years. The estate tax lapsed entirely this year but was set to return Jan. 1 with an exemption of $1 million per person and a maximum rate of 55 percent.

The bill also would keep jobless aid flowing to the long-term unemployed for 13 more months, maintaining extended limits, which now range from 60 weeks in states with less than 6 percent joblessness to 99 weeks in states where the unemployment rate is more than 8.5 percent. Benefits normally last for 26 weeks.

The one-year payroll-tax cut would reduce to 4.2 percent the 6.2 percent Social Security tax levied on income up to $106,800. For a family with $50,000 in annual income, the cut would yield tax savings of about $1,000.

The bill also contains an array of other tax breaks for individuals and businesses, aimed at pumping up the economy.

The tax deal was sealed in back-channel talks between Vice President Joseph Biden and Senate Republican leader Mitch McConnell of Kentucky. It offered a glimpse of a new power dynamic likely to characterize the next two years, as Republicans take control of the House and occupy six more Senate seats.

Before the vote, McConnell denounced the effort by Democrats to approve a $1.1 trillion spending bill that would finance the government through the end of the federal fiscal year on Sept. 30.

He called on Democrats to approve a stopgap spending measure that would last only through the early part of next year and to abandon everything else on their agenda.

Democrats, however, are refusing to back down on their priorities, which include the omnibus spending bill, the New START arms-control treaty with Russia, a bill to repeal the “don’t ask, don’t tell” policy barring open military service by gay men and women, and an immigration measure that would create a path to citizenship for certain illegal immigrants brought to the U.S. as children.

The spending bill, in particular, has incited a contentious battle. Sen. Daniel Inouye, D-Hawaii, chairman of the Appropriations Committee, said he believed he had the votes to pass it. Senate Republicans have denounced the bill, which includes more than 6,000 lawmaker-directed spending items known as earmarks, only to face blistering questions about earmarks they had requested.

Aides to Reid said they had mapped out a path to securing votes on all the bills, which would mean staying in session until next Thursday, two days before Christmas, and potentially returning the week before New Year’s Day.

New York Times reporter Janie Lorber contributed to this report. Information from The Washington Post and The Associated Press also is included.