The measure, which still facesas overgenerous to the wealthy, would spare Americans at every income level from larger tax bills beginning Jan. 1.
With opposition Republicans poised to take control of the House in the next Congress when it convenes early in 2011, Mr. Obama was forced to drop his objections to an extension of lower assessments on upper-income and wealthy Americans. Republicans had vowed with sufficient votes to carry out their promise to let cuts for lower- and middle-income expire as well.
By agreeing with Senate Republicans to extend lower rates for all Americans, he won their promise to back a 13-month extension of jobless benefits for the long-term unemployed.
The bipartisan deal marks a test of how Mr. Obama will govern without his Democratic party in control of both houses of Congress. His readiness to reach accommodation with the opposition Republicans likely will set a pattern for the final half his term leading into the 2012 election.
Despite strong criticism from fellow Democrats, Mr. Obama has made passage of the bill a key year-end priority, calling it essential for the economy as it struggles to recover from the worst recession in decades.
Mr. Obama on Wednesday urged Congress to pass the plan quickly.
"I know there are different aspects of this plan to which members of Congress on both sides of the aisle object. That's the nature of compromise," the president said before meeting with business leaders. "But we worked to negotiate an agreement that's a win for middle-class families and a win for our economy, and we can't afford to let it fall victim to either delay or defeat."
The measure which amounts to a second stimulus package and is estimated to cost $858 billion also cuts 2 percent from payroll taxes, the assessment that goes to finance Social Security pension payments to the retired and disabled.
While senators of both parties overwhelmingly backed the deal by a vote of 83-15 in a test vote, House Democrats continue to balk, especially over the portion of the compromise dealing with taxes on inheritance.
CBS News correspondent Nancy Cordes reports that many House Democrats say, even if the tax deal passes in the Senate on Wednesday, they still want to change some provisions they don't like, particularly a cut in the payroll tax which they say robs the Social Security fund and a cut in the estate tax which they consider a handout to the wealthy.
At the insistence of Republicans, the plan includes a more generous estate tax provision: The first $10 million of a couple's estate could pass to heirs without taxation. The balance would be subject to a 35 percent tax rate.
The lower estate tax infuriated some Democrats who were already unhappy with Obama for agreeing to extend tax cuts for individuals making more than $200,000 and couples making more than $250,000.
"This administration fights for nothing," said Rep. David Wu, an Oregon Democrat.
House Democrats are fuming over extended benefits to the wealthy, but even critics of the package say they expect it to pass as is.
"There's a political reality here," said Democratic Rep. Bill Pascrell of New Jersey. "We can jump up and down all we want about the higher end estate taxes, and I don't think anything's going to change because the Senate isn't going to change it."
The House could take up the bill Wednesday or Thursday, said Rep. Louise Slaughter, chairwoman of the House Rules Committee.
The tax deal moves forward as Congress winds down a final session before the Democrats cede their majority to Republicans in the House. The Senate will remain under Democratic control, but the president's party will hold a much smaller majority.
Mr. Obama needs to get the tax measure out of the way to get to a Senate vote on the New Start agreement with Russia. Republicans vowed to block vote on ratification of the nuclear reduction pact, signed by Mr. Obama and Russian President Dmitry Medvedev in April, until action was taken on taxes.
The Constitution requires that 67 of 100 Senators approve on such a treaty. Mr. Obama has calculated success was more likely in this session than the next when there will be fewer Democratic seats.