Undocumented immigrants in same-sex marriages are perhaps the most polarizing slice of the American populace right now (slightly ahead of NBC's gymnastics commentators).
The federal government does not recognize gay marriage, as established in the Defense of Marriage Act, which Obama has declared unconstitutional. The administration has called on the Supreme Court to repeal the law. In the meantime, though, a same-sex marriage between an American citizen and an immigrant does not make the immigrant eligible for a green card.
Advocates worry that the vagaries of prosecutorial discretion don't ensure that authorities give an immigrant credit for a same-sex relationship. Democrats made a similar push for more specific deportation guidelines in September to which the Department of Homeland Security replied that "LGBT individuals' ties and contributions to the community are taken into account."
This week's effort comes days before the legislators return home to campaign. Good timing, considering the Chick-fil-A controversy has energized both sides of the gay marriage debate, perhaps loosening their pockets as the fall election approaches.