The bipartisan bill, which is under consideration by the Senate Judiciary Committee, would make legal immigration easier for highly skilled immigrants, migrant farm workers and those living in the United States illegally.
What the legislation doesn't include are provisions allowing foreign-born, same-sex partners of U.S. citizens to become permanent residents through application for a green card, The New York Times reported Tuesday.
Gay advocates were disappointed the so-called Gang of Eight senators didn't include such language in the bill and Democrats are considering adding an amendment allowing gay Americans to sponsor green cards.
Republicans warn, though, adding an amendment could cause the bill to fail.
"There's a reason this language wasn't included in the Gang of Eight's bill: It's a deal-breaker for most Republicans," U.S. Sen. Jeff Flake, R-Ariz., said. "Finding consensus on immigration legislation is tough enough without opening the bill up to social issues."
Sen. Marco Rubio, R-Fla., said adding an amendment "will virtually guarantee it won't pass."
"This issue is a difficult enough issue as it is. I respect everyone's views on it. But ultimately, if that issue is injected into this bill, the bill will fail and the coalition that helped put it together will fall apart," he said, quoted by Politico.