President Donald Trump fired off against the Senate in a social media post Friday evening and called on them not to "leave town until they have a Deal."

"If they can’t reach a Deal, the Republicans should terminate the Filibuster, IMMEDIATELY, and take care of our Great American Workers!" he posted.

Senate Republicans, heading into a leadership meeting on Friday afternoon, projected that the Democratic offer made by Senate Minority Leader Chuck Schumer earlier Friday is a "non-starter" -- at least in its current form.

"I think everybody who follows this knows that's a nonstarter. There is no way. The Obamacare extension is the negotiation. That's what we're going to negotiate, once the government opens up," Senate Majority Leader John Thune said.

Sen. Rick Scott, a Florida Republican, seemed angered by the proposal.

"They're okay with people needing food, not getting food stamps, but they want to make sure people get health care subsidies that could be worth a million bucks. How? Tell me how that makes any sense. That's exactly what they're doing," he said.

Still, Republicans say the offer is a step in the right direction. They said it shows Democrats are willing to negotiate.

"I think it's an indication that they're, yeah, I mean, they're feeling the heat, and they know that their last proposal was unserious and unrealistic. But so I guess you can characterize that as progress, but I just don't think that it gets anywhere close to what we need to do here, and they know it," Thune said.

-ABC News' Allison Pecorin and Isabella Murray

Senate Majority Leader John Thune told reporters after a fiery floor speech on Friday that the Senate will "roll into the weekend."

Earlier in the day, Thune said he expected the Senate to be in town this weekend.

"Our members are going to be advised to be available if in fact there is a need to vote, and we will see what happens and whether or not, over the course of the next couple of days, the Democrats find a way to reengage again," Thune had said.

The House will officially be out of session again next week amid the government shutdown for the eighth week in a row. The lower chamber held its last vote on Sept. 19 -- 49 days ago.

The House was slated to be on recess next week.

During the Friday afternoon pro forma session, the clerk read a message from the speaker of the House designating Monday, Nov. 10 through Sunday, Nov. 16 as a "district work period."

Speaker Mike Johnson has kept his chamber on a 48-hour notice return, meaning the House will be out unless there is Senate action to resolve the government shutdown.

There are no committee hearings or markups scheduled in the House next week.

-ABC News' Lauren Peller

Senators will once again vote on Tuesday whether to reopen the government. This will be the 14th time that senators cast votes on a clean, House-passed bill that would reopen the government until Nov. 21.

It would need 60 votes to advance. So far, in previous votes, Sen. Rand Paul has been the lone Republican to vote against this bill and Democrats Catherine Cortez Masto, John Fetterman and independent Angus King have voted for it. Republicans remain in the hunt for five additional Democrats to flip sides and vote to advance this bill.

Though there have been murmurs on Capitol Hill of promising talks between rank-and-file members, no other Senate Democrats have said they intend to switch their vote.

-ABC News' Allison Pecorin