WASHINGTON (AP) — Senators get their first chance Monday to vote on the tax-cut deal struck by President Barack Obama and Republicans in a test vote that is expected to get widespread support.

But House Majority Leader Steny Hoyer said House Democrats may try to change the bill to make the estate tax less generous to wealthy heirs. Hoyer stressed that he expects the House to pass the package. But, he said, House Democrats are unhappy with a provision that would allow estates as large as $10 million to go untaxed.

"I think we're going to have a vote on the Senate bill, with possible changes," Hoyer said Monday during a discussion at the National Press Club. "We may have it with amendments, we'll see what the process is."

The No. 2 Senate Democrat, Dick Durbin of Illinois, said a "good cross-section" of senators in his party are ready to accept the deal.

Monday's vote is expected to lead to passage in the Senate Tuesday or Wednesday. The bill would then go to the House.

The legislation would avert a Jan. 1 increase in income taxes for nearly all Americans, including middle and high earners. The package also would renew a program of jobless benefits for the long-term unemployed and put in place a one-year cut in Social Security taxes.

"Everybody understands what it would mean for the economy if we don't get this done," Obama adviser David Axelrod said.

"We believe that when it comes back to the House, that we will get a vote, and that we'll prevail there, because at the end of the day, no one wants to see taxes go up on 150 million Americans" on New Year's Day, Axelrod said. "No one wants to see 2 million people lose their unemployment insurance."

While many House Democrats have criticized the tax deal, Axelrod said he didn't foresee "major changes" being made by the House.

At the insistence of Republicans, the plan includes a more generous estate tax provision: The first $5 million of a couple's estate could pass to heirs without taxation, and an additional $5 million 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The estate tax was repealed for 2010.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 estates above $1 million, $2 million for couples.

The lower estate tax infuriated Democrats who are already unhappy with Obama for agreeing to extend tax cuts at incomes of more than $200,000 for individuals and $250,000 for couples. Some Democrats say the tax breaks will unnecessarily add to the rising federal deficit. In all, the package would cost about $858 billion, according to a congressional estimate.

Axelrod spoke on ABC's "This Week," CBS' "Face the Nation" and CNN's "State of the Union."