Rep. Chris Van Hollen of Maryland, who heads the Democratic Congressional Campaign Committee, told reporters that the package will get a vote in the House despite a threat by House Democrats last week to prevent it from reaching the floor.
"What form the bill comes to the floor in is something that's under discussion and debate," Van Hollen said, later adding that the House "will have an opportunity to work its will, but there will be as I say discussions as to the form it takes when it arrives for that vote."
Two other House Democrats, Rep. Jim McDermott of Washington and Rep. Elijah Cummings of Maryland, agreed on CNN's "State of the Union" that the House would take up the package, even though some Democrats would vote against it.
The remarks showed a softening in the sometimes vitriolic Democratic opposition so far to the tax and benefits package that Obama announced last week.
At a closed meeting Thursday where members shouted "just say no," House Democrats decided against even considering the deal, raising questions about Obama's influence in his own party and whether any agreement with Republicans could win congressional approval in the current lame-duck session.
With Republicans winning control of the House and diminishing the Democratic majority in the Senate in the new Congress that convenes in January, Obama and his top aides argue that a deal must be cut and delivered now.
On Sunday, White House senior adviser David Axelrod ruled out any major changes to the tax package, telling CNN's "State of the Union" that it was time to move forward on a compromise that includes elements distasteful to each side.
The focus must be on what is best for the country right now, rather than scoring political points or settling political scores, Axelrod said.
"You can focus on what you don't like and ... cut your nose off to spite your face, and that would be the wrong thing to do," Axelrod said, adding that he expected Congress to approve the deal.
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