The spending bill, which extends current government funding levels, is already facing skepticism from both sides of the aisle. For Republicans, it lacks the steep cuts they hoped their new leader would be willing to push; for Democrats, it may not avoid a 1 percent cut that could kick in early next year under the terms of a debt deal reached over the summer. And it kicks the current spending battle down the road yet again.

Johnson told members he plans to bring the plan up for a floor vote on Tuesday, but if he hopes to pass the unusual proposal, which sets up two different funding deadlines for different parts of the government (one on Jan. 19, the other Feb. 2) he’ll need buy-in from House Democrats — putting him in exactly the same position as former Speaker Kevin McCarthy, who was promptly ousted after moving a spending bill with more votes from Democrats than from his own party.

But McCarthy has hope for his successor, he told CNN’s Manu Raju, during an interview that aired Sunday. “Who are you going to replace him with?” McCarthy said, alluding to House Republicans’ repeated struggles to elect a leader.

However, even attracting Democratic support in the first place will be difficult. As one House Democrat, Rep. Madeleine Dean (D-Pa.), put it on MSNBC’s “The Sunday Show": “I’m not interested in that.”

Senate Democrats, however, have been careful to leave the door open to potentially supporting the GOP bill — and Murphy continued to do just that on Sunday. “I don’t like what the House is talking about but I’m willing to listen,” he said.

Still, Murphy was not all that hopeful.

“I don’t think anybody can predict what happens in the House of Representatives today. That place is a political dumpster fire right now,” he said.