With the immigration bill on its way to the Senate Judiciary Committee for a vote next week, it faces another obstacle–recognition of same-sex unions.

Gay rights advocates have garnered a number of victories over the last several months, particularly in gaining increased recognition of same-sex marriages in a number of states, but to listen to Republican senators, attaching same-sex unions to the immigration measure is a no-no.

“There’s a reason this language wasn’t included in the Gang of Eight’s bill,” said Sen. Jeff Flake, R-Ariz. “It’s a deal-breaker for most Republicans. Finding consensus on immigration legislation is tough enough without opening the bill up to social issues.”

The “Gang of Eight” Flake referenced are the eight senators–four Democrats and four Republicans–who have been diligently working to resolve the impasse blocking immigration reform. Currently, they have introduced an 844-page bill that would make it easier for 11 million undocumented immigrants to gain citizenship.

Sen. Marco Rubio, R-Fla., a member of the bipartisan group, agreed with Flake, and added that getting this far has been troubling enough. “If that issue is injected into this bill, this bill will fail. It will not have the support. It will not have my support.”

There has been no recent response to this issue from Sens. Chuck Schumer, D.-N.Y., or Richard Durbin, D-Ill.–two strong proponents of gay rights. A few weeks ago, there was notice from gay advocates of applying pressure to Schumer and other Democrats to own up to the Uniting American Families Act (UAFA), which would end restrictions on Americans in bi-national same-sex relationships from having their partners or spouses treated the same as married heterosexual spouses and partners under U.S. law.

Earlier this year, President Barack Obama proposed that the UAFA measure be included in the bill. According to Immigration Equality, an advocacy group for LGBT and HIV-infected immigrants, there are estimates of 36,000 bi-national same-sex couples living in the U.S. Even those in a valid marriage with a same-sex American spouse are prevented from gaining permanent status in America. Their only hope is that the U.S. Supreme Court will strike down the 1996 Defense of Marriage Act and eradicate that barrier. Oral arguments on the issue were heard last month.