A pair of Republican senators introduced legislation on Friday that would pair President TrumpDonald John TrumpPentagon update to missile defense doctrine will explore space-base technologies, lasers to counter threats Giuliani: 'I never said there was no collusion' between the Trump campaign and Russia Former congressmen, RNC members appointed to Trump administration roles 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 PortmanSenators look for possible way to end shutdown GOP reasserts NATO support after report on Trump’s wavering Leaders nix recess with no shutdown deal in sight MORE (R-Ohio) and Jerry MoranGerald (Jerry) MoranOn The Money: Shutdown Day 26 | Pelosi calls on Trump to delay State of the Union | Cites 'security concerns' | DHS chief says they can handle security | Waters lays out agenda | Senate rejects effort to block Trump on Russia sanctions Senate rejects effort to block Trump on Russia sanctions Overnight Defense: Trump faces blowback over report he discussed leaving NATO | Pentagon extends mission on border | Senate advances measure bucking Trump on Russia sanctions 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." 

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 GrahamCentrist efforts to convince Trump to end shutdown falter Overnight Defense: Four Americans killed in Syria suicide attack | State of the Union becomes latest shutdown flashpoint | Missile defense review on track for Thursday release White House condemns 'terror attack' that killed US troops in Syria 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.