At around 8:50 p.m. on Sunday night, a spokesperson for Senate Majority Leader Mitch McConnell came out to the throng of reporters spending their weekend in the corridors of the Capitol and announced that McConnell would be speaking on the floor shortly. It was the white smoke no one was quite sure would come. All day, McConnell had been taking meetings with an impeccably dressed Arizona Sen. Jeff Flake and a shabbily dressed South Carolina Sen. Lindsey Graham, who had taken it upon themselves to act as liaisons between the Democratic and Republican leaders.

There was no deal to announce, but an offer had been extended from Republicans, leaving Democrats to ponder whether to capitulate or further entrench their risky position before a noon vote on Monday.

The announcement read by McConnell was one that Flake and Graham had been negotiating all day. If Democrats reopened the government on the bill under consideration, which would fund the government until Feb. 8, and there was no breakthrough on an immigration deal before then, it would be McConnell’s “intention” to open debate on immigration and, as Texas Sen. John Cornyn said afterward, allow “the Senate to work its will.” In other words, the Senate would take up a shell bill and various immigration proposals, like the bipartisan legislation Flake and Graham have introduced, or more partisan alternatives, could be called up as amendments. House Speaker Paul Ryan, however, has made no commitments that he would call up the winner of the Senate process for a vote in the House.

McConnell then asked for a 10 p.m. cloture vote on the Senate bill. Schumer objected but didn’t object to McConnell’s next proposal for a vote at noon Monday. (McConnell’s and Schumer’s staffs had choreographed this sequence just minutes before.) This guarantees that federal workers will be furloughed when they wake up for the first workday of the shutdown.

Cornyn, who was notably more conciliatory to the alleged instigator of the “Schumer Shutdown” than he had been in recent days, explained that it was fair enough for Schumer to want time to “chew things over” with his caucus.

Democrats may need all of that time.

Schumer, speaking on the floor, stated that the two sides had “yet to reach an agreement on a path forward that would be acceptable to both sides.” McConnell’s offer does not meet what Democrats have demanded, which is an agreement not just on the fate of Deferred Action for Childhood Arrivals recipients but also the outlines for a plan on spending caps, disaster relief, and other bottlenecked issues. Securing Senate floor time doesn’t secure any floor time in the House, where the hardliners seemingly have control over Ryan and the immigration debate. And a promise to consider immigration after Feb. 8, rather than before it, takes away their leverage over the next piece of funding legislation.

But it does give Democrats an off-ramp from their gamble, which some of them could regret turning down if they don’t take it now. Republicans on the Hill believe they have Senate Democrats over a barrel, and the stench of sweating Senate Democrats up for re-election this year in Trump-won states is becoming noticeable. Some of them will want to take the face-saving gesture to end this before any permanent damage is done.

Though there’s no guarantee of a House vote, one can envision at least an endgame that squeezes House Republicans: Because the Gang of Six bipartisan immigration bill, or one like it, is probably the only bill that can get the 60 votes necessary to escape the Senate floor process, it would arrive at the House’s doorstep as the DACA expiration date nears. House Republicans could try to pass a conservative alternative, like the Goodlatte-Labrador bill, but even if it passed, it would die in the Senate. The Gang of Six bill, by contrast, could pass the House. The pressure for preserving protections for DACA beneficiaries, as everyone in Congress claims to want, would fall squarely on Ryan’s shoulders.

Flake, who along with Graham will be flipping to “yes” on Monday’s vote, said he personally will be trying to persuade Democrats to join him. What will he tell them?

“That we actually did get something here,” Flake told reporters. “One, we got the date moved up [from Feb. 16 to Feb. 8], and two, for the first time, we got the majority leader off of, ‘We can only move [an immigration bill] if the president agrees.’ That shouldn’t be that difficult, in my view, but it is.”

Plenty of Democrats won’t want to go along with this. But it might be enough to peel off seven additional Democrats that Republicans would need to get to 60 on the Monday cloture vote.

Cornyn, who had been more pessimistic than Flake and Graham for much of the day, was asked after McConnell’s offer if he was confident that cloture would be invoked.

Maybe prematurely.

“I’m optimistic,” he said.