"I don't think it's any secret that in the past, unions killed immigration reform," Sen. Marco Rubio told Politico. "I think because of pressure from some of their members, they've at least publicly changed their stance on this. But I don't think they are doing cartwheels over this."
Labor unions laid blame for the stalemate at the feet of Republicans.
"We have conceded on so many different grounds. [Republicans] want to pave the path to citizenship with poverty," AFL-CIO spokesman Jeff Hauser told Reuters this week.
The AFL-CIO has stressed its commitment to immigration reform and a path to citizenship for undocumented immigrants. But last week, Ana Avendaño, a top immigration policy aide at AFL-CIO, said that accounting for the future flow of lesser-skilled immigrant workers "is arguably really not necessary to be in the package."
"Programs like the bracero program or temporary guest-worker programs where individuals were tied to an employer, they got exploited," the AFL-CIO's Trumka told Univision earlier this month.
But senators working out the deal have long said that a low-skilled worker program is an essential part of reform, underscoring the importance of the latest agreement.
"We recognize that to prevent future waves of illegal immigration a humane and effective system needs to be created for these immigrant workers to enter the country and find employment without seeking the aid of human traffickers or drug cartels," reads the "Gang of Eight's initial immigration framework.
ABC News correspondent Jeff Zeleny and Emily DeRuy contributed to this report.