A pair of Republican senators introduced legislation on Friday that would pair President TrumpDonald John TrumpFeinstein, Iranian foreign minister had dinner amid tensions: report The Hill's Morning Report - Trump says no legislation until Dems end probes Harris readies a Phase 2 as she seeks to rejuvenate campaign 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 PortmanThe Hill's Morning Report - White House, Congress: Urgency of now around budget WANTED: A Republican with courage Companies warn Trump trade war is about to hit consumers MORE (R-Ohio) and Jerry MoranGerald (Jerry) MoranOn The Money: Judge upholds House subpoena for Trump financial records | Trump vows to appeal ruling by 'Obama-appointed judge' | Canada, Mexico lift retaliatory tariffs on US | IRS audit rate falls GOP senator calls for resolution of trade dispute: 'Farmers and ranchers are hurting' Frustrated GOP senators want answers from Trump on Iran 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 GrahamThreat of impeachment takes oxygen out of 2019 agenda Graham urges Trump not to abandon infrastructure talks with Democrats Congress, White House near deal on spending, debt limit 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.