Senators get their first chance Monday to vote on the tax-cut deal struck by President Barack Obama and Republicans, but whatever the outcome of the test vote, the White House expects the bill to pass by year’s end.

“Everybody understands what it would mean for the economy if we don’t get this done,” Obama adviser David Axelrod said Sunday. 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.

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.

“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.

Maryland Rep. Chris Van Hollen, a member of the Democratic leadership who represented the House in negotiations with the administration, made clear that Democrats strongly object to extending breaks to estates as large as $5 million. He said the package will be taken up in the House in some form, but there would be an effort to change the estate tax provision.

“We’re not talking about blocking the whole thing,” Van Hollen said.

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.

That provision 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, and who say the tax breaks will unnecessarily add to the rising federal deficit. In all, the package would cost about $855 billion, according to a preliminary congressional estimate.

Axelrod spoke on ABC’s “This Week,” CBS’ “Face the Nation” and CNN’s “State of the Union.” Van Hollen appeared on “Fox News Sunday” and Durbin was on CNN.