Hill, in a brief interview with The Hill, said he wanted to pass a budget document. He added that groups in the House Democratic Caucus left of the Blue Dogs have concerns aside from low spending levels.
Senate Budget Committee Chairman Kent Conrad (D-N.D.) also said Tuesday that the chance of a budget resolution this year is "fading," though he and House leaders have also said they're hopeful a budget could be passed.
The budget resolution sets discretionary spending levels for the next year and lays out the majority's fiscal policies for several years. The budget also serves as the first necessary step in the reconciliation process that's used to push contentious legislation through the Senate with a simple majority instead of 60 votes.
Instead of a budget resolution, Democrats could turn to a deeming resolution that sets spending levels for the next year but lacks the other budget features, Hill and Conrad said Tuesday.
Hill said the spending cuts in a deeming resolution could be deeper than they would be in a traditional budget resolution.