“I think the next step is going to be we’re going to have a budget on the floor maybe by the third week of March,” said Sen. Mark Begich (D-Alaska).

But Begich said he’s not optimistic the sequester will be solved anytime soon.

“Anything’s possible, but there’s not a mechanism yet,” he said.

Democrats acknowledge a budget plan passed by the Senate alone would not be sufficient. Only a bicameral budget resolution negotiated by the Senate Democratic and House Republican leaders could provide enough assurance of future savings to replace the sequester.

“You would have to have a bipartisan, bicameral budget resolution to fix the sequester,” said Sen. Jeff Sessions (Ala.), the ranking Republican on the Budget Committee. “It would be a long shot. I won’t say it’s impossible.”

Negotiations to forge a joint resolution with House Republicans could easily drag into the summer.