The White House and the second-ranking House Democrat expressed confidence on Monday night that the House would pass a tax-cut package, likely by the end of this week.

House members who'd previously opposed the deal are likely to ultimately back President Obama's tax-cut deal with congressional Republicans, said House Majority Leader Steny Hoyer (D-Md.).

"The legislative process, as the president said today, is a series of taking some things you want and taking some things you don't want, because you think there's a net plus in the action that you're taking," the No. 2 House Democrat said on MSNBC. "So I think that's what happened in the Senate. I think that may well happen and probably will happen in the House."

The tax-cut deal, which extends all expiring income tax rates for two years in exchange for an extension of unemployment benefits and some middle-class tax breaks, cleared a procedural hurdle in the Senate on Monday in a strong, bipartisan vote. Eighty-three senators voted to advance the deal.

House Democrats have been more boisterous in their opposition to the deal, though, which they viewed as too quick and too substantial a cave to GOP demands. In particular, a number of members have hoped for a change to the bill's formulation of the estate tax.

But the White House has launched an all-out offensive to pressure lawmakers to approve the tax deal. Without congressional action, taxes would go up on Jan. 1, and create a massive political headache for Obama and Democrats in Congress.

Congress is likely to wrap up its work by week's end on not just taxes, said White House press secretary Robert Gibbs, but also other priorities like the New START Treaty, and perhaps a measure to repeal "Don't ask, don't tell."

"My guess is that the legislation ... will be the basic framework that the House eventually takes up, and I think the legislation at the House will eventually pass," he said in a separate appearance on MSNBC. "That ensures we also have time for the Senate to deal with some very important issues like the New START Treaty, getting that ratified.

"So, I think certainly by the end of this week, we're going to see bipartisan agreement and bicameral agreement on getting this stuff done," Gibbs added.

Lawmakers are hoping to get out of Washington by Friday, Dec. 17, and avoid the late-season Christmas holiday work that they'd endured last year at the height of the congressional battle over healthcare reform.