WASHINGTON — Far-reaching legislation to avert a Jan. 1 income-tax increase for millions won overwhelming support in a Senate test vote on Monday, backed by an uneasy and unusual alliance between the White House and lawmakers in both parties.

Even before the vote was complete, President Barack Obama said the show of support "proves that both parties can in fact work together to grow our economy and look out for the American people."

Senate passage, expected within a day or two, would set up a final showdown in the House between Obama and liberals in his own party who want the White House to scale back the billions the bill includes in relief ticketed for the rich.

In his remarks, the president gave no indication he was willing to accept further changes to the measure he negotiated with senior Republicans.

"I understand those concerns," he said of the objections from some of his usual allies in Congress. "I share some of them. But that’s the nature of compromise, sacrificing something that each of us cares about."

Despite strong criticism from fellow Democrats, Obama has made passage of the bill a key year-end priority, essential for the economy as it struggles to recover from the worst recession in decades.

In the Senate, Majority Leader Harry Reid, D-Nev., and his GOP counterpart, Mitch McConnell of Kentucky, were joint sponsors of the bill, a symbolic gesture of bipartisanship on an issue that produced nothing but gridlock until midterm elections gave Republicans additional leverage in negotiations.

"We’re telling the American people to keep money that’s rightfully theirs, so they can spend it and invest it as they please," said McConnell.

In a jab at Democrats, he added, "This is an important shift, and the White House should be applauded for agreeing to it."

Sen. Max Baucus, D-Mont., who chairs the Senate Finance Committee, said, "This bipartisan compromise is about creating jobs. Extending middle class tax cuts will help create jobs. … Job creation needs to be our number one priority."

The bill needed 60 votes to clear a procedural hurdle. It achieved that level quickly in a long roll call, although no final tally was expected for hours.

The bill would provide a two-year reprieve in the tax increases scheduled to take effect on Jan. 1 at all income levels, reduce Social Security taxes for every wage earner in 2011 and extend an expiring program of jobless benefits for the long-term unemployed. The estimated cost, $858 billion over two years, would be added to already-huge federal deficits.

The measure represents a reach across party lines after two years of political combat in which Republicans wanted a permanent extension of all the tax cuts enacted when George W. Bush was president, while Democrats insisted rates be permitted to rise on incomes over $200,000 for individuals and $250,000 for couples.

Despite the bipartisanship in the Senate, disgruntled House Democrats have vowed to block a final vote unless the legislation is changed to scale back the tax relief for the nation’s wealthiest.

"I think we’re going to have a vote on the Senate bill, with possible changes," House Majority Leader Steny Hoyer, D-Md., said. "We may have it with amendments, we’ll see what the process is."

The compromise emerged a week ago after private talks involving the White House and top leaders in Congress, including Republicans who emerged from midterm elections with significantly increased strength.

In the days since, Obama has drawn strong criticism from liberals unhappy that he agreed to changes in the estate tax and income tax that will benefit the rich. Firing back, he said failure to compromise would produce gridlock at a time the economy is still frail and unemployment is at a persistently high rate of 9.8 percent.

The administration’s outgoing top economic adviser, Lawrence Summers, said in a speech a few hours before the vote that the agreement should increase consumer spending and help the economy "now and for the next several years."

On the other end of the political spectrum, some conservatives have spoken out against the bill, saying that the renewal of jobless benefits should be offset by spending cuts elsewhere in the budget.

In fact, even supporters of the bill were at pains to point out parts they found objectionable.

Baucus singled out the decision to leave tax rates unchanged on upper income earners.

Sen. John McCain, R-Ariz., highlighted a series of energy tax breaks added to the bill late last week, including an extension of the federal subsidy for ethanol.

McConnell cited "the Democrats’ insistence that we borrow the money we need to pay for a further extension of unemployment insurance. In my view, if both parties agree that the debt is a serious problem, we shouldn’t be writing checks that we don’t have the money to cover."

Many House Democrats objected strongly to a change in the estate tax that Republicans won as part of the deal. The first $5 million of a couple’s estate could pass to heirs without taxation, and an additional $5 million could be passed along for the spouse. The balance would be subject to a 35 percent tax rate.

The estate tax was repealed for 2010. But under current law, it is scheduled to return next year with a top rate of 55 percent on the portion above $1 million, $2 million for couples.