He added that hundreds of thousands of immigrants have a "concern and a fear" about what will happen to them if Trump roles back Obama's executive action.
In addition to Durbin and Graham, Sens. Lisa MurkowskiLisa MurkowskiTrump’s Army pick faces tough confirmation fight Republican Sen. Collins considering run for Maine governor in 2018 Alaska senators push bill to allow Arctic drilling MORE (R-Alaska), Dianne FeinsteinDianne FeinsteinHotel industry details plans to fight Airbnb Congress needs a do-over on fraud-laden 'Immigrant Investor' program Ginsburg appears to refer to Graham as one of 'the women of the Senate' MORE (D-Calif.) and Jeff FlakeJeff FlakeTrump wall faces skepticism on border No Congress members along Mexico border support funding Trump's wall Obama-linked group launches ads targeting Republicans on immigration MORE (R-Ariz.) are backing the bill.
The legislation would allow undocumented immigrants who are eligible for DACA to apply for "provisional protected status" if they pay a fine and undergo a background check.
The law would sunset after three years.
"If you have DACA now you would receive provisional protected status until your DACA expires and you can apply for an extension," Durbin said.
The legislation won't pass the Senate this year, with lawmakers expected to leave town as soon as Friday. Durbin indicated Friday they would reintroduce the bill early next year.
Graham announced late last month that he was working on the bill with Durbin, arguing it would buy "Dreamers" time as lawmakers try to pass a broader comprehensive immigration bill.
Graham urged Trump to back the bill on Friday, arguing it would help pave the way to provide legal status through "the proper constitutional process."
“They got brought here at a very young age, they’ve worked here, they’ve gone to school here. Some were good students. Some have wonderful jobs. And they’re in never-never land because they don’t know what’s going to happen," he told Time magazine.
Trump came under fire during the campaign for taking a hard-line on immigration, pledging to deport roughly 11 million undocumented immigrants. He's walked that back since, noting he would focus primarily on those with criminal records.
Friday's legislation was quickly endorsed by outside groups.
Frank Sharry, the executive director of America’s Voice, called the bill an "important step."
It's unclear if, or when, the Graham-Durbin bill could be taken up next year.
Asked about moving DACA legislation next year, Sen. John CornynJohn CornynTrump wall faces skepticism on border No Congress members along Mexico border support funding Trump's wall Obama-linked group launches ads targeting Republicans on immigration MORE (R-Texas) told reporters Thursday that it was a "question of sequence" and that it should come after border security.
"But I don't think [Trump is] interested in hurting the children who came with their parents," he said. "They're not culpable of anything. I think there needs be a reasonable way to deal with, and I think he's indicated he's open to that."
House Speaker Paul RyanPaul RyanPelosi: 'Of course' Dems can be against abortion Five fights for Trump’s first year Sunday shows preview: Trump stares down 100-day mark MORE (R-Wis.) added separately that Republicans won't "pull the rug out from under” undocumented immigrants brought to the U.S. as children.