A pair of Republican senators introduced legislation on Friday that would pair President TrumpDonald John TrumpSanders apologizes to Biden for supporter's op-ed Jayapal: 'We will end up with another Trump' if the US doesn't elect progressive Democrats: McConnell impeachment trial rules a 'cover up,' 'national disgrace' MORE's border funding request with a fix for an Obama-era immigration program, as lawmakers hunt for an end to the ongoing partial government shutdown.

The bill from Sens. Rob PortmanRobert (Rob) Jones PortmanHillicon Valley: Biden calls for revoking tech legal shield | DHS chief 'fully expects' Russia to try to interfere in 2020 | Smaller companies testify against Big Tech 'monopoly power' Bipartisan group of senators introduces legislation to boost state cybersecurity leadership Senate approves Trump trade deal with Canada, Mexico MORE (R-Ohio) and Jerry MoranGerald (Jerry) MoranOvernight Defense: War powers fight runs into impeachment | Kaine has 51 votes for Iran resolution | Trump plans to divert .2B from Pentagon to border wall War powers fight in Senate runs squarely into impeachment Third GOP senator says he'll support Iran war powers resolution MORE (R-Kan.) would include a $25 billion trust fund for border security, including fencing and physical barriers, while codifying the Deferred Action for Childhood Arrivals (DACA) program for current recipients. 

Moran said the legislation would return negotiations "to the basics of what a majority of my colleagues and the president support." 

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Portman added that he believed the legislation was a "fair and reasonable solution" as Congress and the White House try to find an escape hatch from the entrenched shutdown fight.

"I believe we have a responsibility to resolve this issue, and this legislation is a fair and responsible solution that could get the necessary votes to become law," Portman said. 

The administration announced in 2017 that it was ending DACA, which allows certain immigrants who do not have legal status to stay in the United States to work and go to school. 

Under the Portman-Moran bill, DACA would be codified for current recipients, who would need to renew their status every two years. 

The bill would be unlikely to get enough support from Democrats to get 60 votes in the Senate — much less pass through the Democratic-controlled House. Portman introduced similar legislation last year, but it was panned by Democratic leadership.   

Portman publicly pitched his idea earlier this month as lawmakers began to float an immigration deal as a path out of the shutdown fight, saying it would be a "win-win" for both sides.

“That seems to me to be one where Republicans and Democrats could each find some opportunity for victory,” he said. “I think this is an example where both sides can give a little [and] we don’t have a shutdown anymore.”

The introduction of the GOP immigration proposal comes after a last-ditch effort by a group of moderate Senate Republicans, including Portman, to find a deal that would link a DACA fix with border funding. The effort unraveled on Thursday amid pushback from Trump. 

As part of those negotiations, led by Sen. Lindsey GrahamLindsey Olin GrahamWhite House appoints GOP House members to advise Trump's impeachment team Hypocrisy is the currency of the realm for GOP in the age of Trump Lawmakers push back at Pentagon's possible Africa drawdown MORE (R-S.C.), senators had discussed binding Trump's request for more than $5 billion for the wall to a DACA fix, while letting most or all of the government reopen. 

But Trump indicated to lawmakers this week that he wasn't interested currently in making a DACA deal and Vice President Pence reiterated to reporters on Thursday that the administration wants to let the current legal fight over the program play out. 

The shutdown, which affects roughly one-quarter of the federal government, entered its 21st day on Friday.