"The message is: Open the government, vote on the Senate bill," said Rep. Rob Andrews (D-N.J.), who heads the Democratic Steering and Policy Committee.
Pressured by conservative Republicans, GOP leaders have insisted that provisions scaling back President Obama's 2010 healthcare law be included as part of legislation to reopen the government. They've accused Democrats of refusing to negotiate, leading to Tuesday's shutdown.
Democrats counter that they compromised in accepting the sequester-level baseline of $986 billion, which was contained in the Republicans' initial continuing resolution (CR) and has been endorsed by Democratic leaders in both the House and Senate.
"The president has been clear. We've compromised; we've come down to their number," Rep. John Larson (Conn.), former head of the House Democratic Caucus, said Thursday. "And they're not going to be held hostage by what amounts to one senator, maybe two, and about 40 people in the House. Otherwise, it sets an unbelievable precedent."
Still, there's a group of liberal Democrats who are ready to reject the Senate's CR because it contains the across-the-board sequester cuts. The liberals say the sequester-level spending threatens the effectiveness of numerous government programs.
The office of Rep. Raul Grijalva, head of the Congressional Progressive Caucus, said the Arizona Democrat will oppose a clean CR.
"That is too low for him," Grijalva spokesman Adam Sarvana said.
Meanwhile, centrist lawmakers in both parties are pushing their leaders to consider the elimination of a medical device tax, which helps fund ObamaCare, as a potential way to break the impasse.
Republicans had tried to move such a provision over the weekend, but it was rejected by Democrats who opposed the lack of an offset.
Reps. Ron KindRon KindJunior Dems plot strategy as leadership vote looms Ryan: Pacific deal can't be fixed in time for lame-duck vote House Democrat expects support to grow for Pacific trade deal MORE (D-Wis.) and Charlie Dent (R-Pa.) outlined their medical-device strategy Thursday, offering to cover the $30 billion cost with a pension-related provision passed by the Senate Transportation Committee in June.
At Thursday's meeting with Democrats, however, party leaders dismissed that strategy, arguing that changes to ObamaCare should be taken up on their own, not as part of the debate over the shutdown and debt-ceiling hike.
Larson said the device-tax repeal is "one of those likely things that you could envision happening" with bipartisan support, "out of the context of [putting] the gun to your head."
Kind conceded he has some convincing to do.
"We still have a little bit of work to do," he said.