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 on Thursday after a final, and seemingly futile, effort to change a provision that benefits wealthy estates.

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

It was the first concrete product of a new era of divided government and acid compromise.

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

“We will make our point,” Ms. Pelosi said at a news conference Wednesday evening, in which she repeated 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. Republicans have said they will not accept any change.