Rubio discussed immigration reform with more than two dozen conservative grassroots leaders in a closed-door meeting on Capitol Hill on Tuesday, according to an aide to the senator.
Most of the activists are backing the reform effort, the aide said.
Durbin acknowledged Tuesday that while he backs Leahy's proposal, it could prove problematic for the larger immigration reform bill.
"There are some problems on the Republican side when it comes to dealing with (lesbian, gay, bisexual and transgender) issues," Durbin told CNN.
The Illinois senator noted the possibility that the upcoming ruling by the U.S. Supreme Court on the federal Defense of Marriage Act could render the whole issue moot.
"The DOMA ruling could change this whole debate," Durbin said. "They could eliminate DOMA and impose obligations on our federal government (relating to) same gender marriage, and that would dramatically change what we're trying to achieve."
Fitz said Leahy will ultimately "find the right way forward."
"The Republican-controlled House will never accept (his same-sex amendment) as part of their bill," he said. Leahy's "not going to tank this bill."
Regardless, it is significantly easier for Leahy to add the amendment to the bill while it is being considered by the Judiciary Committee.
Democrats hold a 10-8 majority on the panel, and can approve changes on a strict majority basis if necessary.
In contrast, controversial amendments taken up by the full Senate are virtually certain to face a 60-vote threshold. The Democratic caucus only controls 55 seats in the 100-member chamber.
Backers of the bill have been hoping to win as many as 70 votes in the Senate, in order to give the bill bipartisan momentum heading into the more skeptical, GOP-controlled House.
A bipartisan group of eight House members is currently working on its own immigration reform plan.