A group of moderate senators is pitching a three-week stopgap bill as an off-ramp to the partial government shutdown in exchange for Congress agreeing to work on a border security plan during that period.

The proposal spearheaded by Sens. Ben Cardin Benjamin (Ben) Louis CardinPPP application window closes after coronavirus talks deadlock Congress eyes tighter restrictions on next round of small business help Senate passes extension of application deadline for PPP small-business loans MORE (D-Md.) and Lisa Murkowski Lisa Ann MurkowskiSenate Republicans face tough decision on replacing Ginsburg What Senate Republicans have said about election-year Supreme Court vacancies McConnell says Trump nominee to replace Ginsburg will get Senate vote MORE (R-Alaska) comes after the Senate on Thursday rejected both a White House-backed plan to provide $5.7 billion for a border wall and a separate plan that would have temporarily reopened the government through Feb. 8.

"We need to pass a short-term, three-week clean CR [continuing resolution] so that we can have time to consider the president's request and work together on a bipartisan border package," Cardin said.

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Murkowski added that the two Senate votes on Thursday were "messaging votes," rather than proposals designed to get the 60 votes needed to pass. She added that while senators need to work together to resolve the border fight, "you can't do it when the government is shut down."

"Allow us then to go through whether it's the appropriations process, the Judiciary Committee process, but allow us to do the business of the United States Senate, to do the business of legislating. But let's also allow the business of the government to proceed by opening up the government right now," Murkowski added.

Trump has previously indicated he is not interested in agreeing to temporarily reopen the federal government and White House press secretary Sarah Huckabee Sanders appeared to immediately pour cold water on the proposal Thursday, even as senators were still discussing it on the floor.

"Leader Mitch McConnell Addison (Mitch) Mitchell McConnellObama calls on Senate not to fill Ginsburg's vacancy until after election Planned Parenthood: 'The fate of our rights' depends on Ginsburg replacement Progressive group to spend M in ad campaign on Supreme Court vacancy MORE [R-Ky.] and Senator Chuck Schumer Chuck SchumerPelosi orders Capitol flags at half-staff to honor Ginsburg Ginsburg in statement before her death said she wished not to be replaced until next president is sworn in Democrats call for NRA Foundation to be prohibited from receiving donations from federal employees MORE [D-N.Y.] are meeting now to see whether or not they can work out of the deadlock. As was made clear to Senator Lindsay Graham, the 3 week CR would only work if there is a large down payment on the wall," she said.

Sen. Lindsey Graham Lindsey Olin GrahamSenate Republicans face tough decision on replacing Ginsburg Democratic senator calls for eliminating filibuster, expanding Supreme Court if GOP fills vacancy What Senate Republicans have said about election-year Supreme Court vacancies MORE (R-S.C.) pitched the three-week plan to Trump during a phone call on Thursday. He said in a statement that the CR must include "a down payment on wall/barrier funding and priorities of Democrats for disaster relief, showing good faith from both sides."

Graham had previously said he spoke with the president about the idea of a three-week continuing resolution on Thursday shortly before the marathon of floor speeches about the idea.