Senators are floating a quick exit from Washington, D.C., after they pass a massive coronavirus stimulus bill that is being finalized Tuesday.

The expectation among senators is that once the chamber passes the legislation, likely on Wednesday, they will not be in session for at least three weeks.

Sen. Roy Blunt Roy Dean BluntMcConnell locks down key GOP votes in Supreme Court fight Murkowski: Supreme Court nominee should not be taken up before election Battle lines drawn on precedent in Supreme Court fight MORE (R-Mo.), a member of GOP leadership, stressed that the decision is up to Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellOcasio-Cortez to voters: Tell McConnell 'he is playing with fire' with Ginsburg's seat McConnell locks down key GOP votes in Supreme Court fight Video shows NYC subway station renamed after Ruth Bader Ginsburg MORE (R-Ky.) but said it was his expectation that the chamber would recess after this week.

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"My guess is we probably don't come in next week and then don't come in the two weeks we're scheduled" to be on recess, Blunt said, adding that they would "use those three weeks to get ready for whatever is phase four."

Blunt said some senators could stay in town to work on additional coronavirus legislation but that "likely we're not in an active daily session."

A source familiar with briefings being given to Democratic senators and top staffers added that “once the Senate is done, they plan to be gone for a while.”

The Senate is currently scheduled to be in session through next Friday, April 3.

After that, the Senate is scheduled for a two-week recess. The chamber was supposed to be out of session last week but changed its plans to remain in Washington to pass a second coronavirus response bill and start crafting a third.

The House left last week without a fixed return date. House leadership is debating clearing the massive stimulus package, which is expected to have a top-line price tag of at least $2 trillion, by unanimous consent, though it's unclear if all 435 members will sign off.

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Blunt added that the Senate would likely stay around to see what the House does on the legislation. House Democrats unveiled their own bill Monday, though House Speaker Nancy Pelosi (D-Calif.) has remained in close consultation with Senate Minority Leader Charles Schumer (D-N.Y.) on Senate negotiations.

Sen. John Thune (S.D.), the No. 2 Senate Republican, predicted that the chamber's schedule would likely be determined "on a week-by-week basis."

"If we could get this wrapped up, I suppose there's a possibility that we could roll into the Easter recess. But I think it will probably be the leader's decision on a week-by-week basis depending on what we need to do to respond to what's going on," Thune said.

Asked if there were other things the Senate needed to clear off its schedule before leaving Washington, he added that it was an "ongoing response to the crisis. Right now, that's really what's driving everything around here."

McConnell hasn't provided any public guidance on what the Senate's schedule looks like after it passes the stimulus package. He's only warned that senators will not leave Washington until they pass the bill.

He was asked during a press conference last week about the Senate's schedule after the stimulus bill passes but declined to comment.

The question of whether senators would remain in the Capitol gained extra urgency this week after Sen. Rand Paul Randal (Rand) Howard PaulSecond GOP senator to quarantine after exposure to coronavirus GOP senator to quarantine after coronavirus exposure The Hill's Morning Report - Sponsored by National Industries for the Blind - Trump seeks to flip 'Rage' narrative; Dems block COVID-19 bill MORE (R-Ky.) became the first known senator to test positive for the virus.

Concerns about the spread of the coronavirus within the Senate are particularly acute because many senators are above 60 and considered an at-risk group. Even as McConnell has encouraged senators to practice social distancing, several have been seen in tight scrums with their colleagues or standing shoulder to shoulder on the floor.

“I believe that our first obligation is to finish our work for the American people. After that, I think it would be wise to accelerate the break that was scheduled for April,” Sen. Susan Collins Susan Margaret CollinsMcConnell locks down key GOP votes in Supreme Court fight Most Americans think winner of election should pick next Supreme Court justice: poll Murkowski: Supreme Court nominee should not be taken up before election MORE (R-Maine) said this week.

Mike Lillis contributed.