GOP balks at LGBT protections in immigration reform

Gutierrez noted that no final legislation has emerged from the bipartisan negotiations on the issue, and suggested that there's still time for Democrats to work the LGBT language into the package.

"It's an issue we're still grappling with," he said. "I don't think we should simply discard it."

But asked directly if any Republicans have been open to the idea, Gutierrez gave a dejected, "No."

Because federal law does not recognize LGBT couples as legitimate families, same-sex couples of dual nationality are not offered the same protections granted to heterosexual couples during deportation proceedings.

Democrats in both chambers are pushing to address that issue. A bill introduced last month by Rep. Jerrold Nadler (D-N.Y.) would empower LGBT American citizens to sponsor visas granting legal residency for their partners, a right they don't currently have. 

“Our Constitution guarantees that no class of people will be singled out for differential treatment – and LGBT Americans must not be excluded from that guarantee," Nadler said at the time. "Moreover, any serious legislative proposal for comprehensive immigration reform absolutely must include gay and lesbian couples and their families."

Gutierrez said Tuesday that he's "hopeful" an immigration reform bill will emerge from the bipartisan talks not long after Congress returns next month from the Easter recess.

"We are under a time pressure to resolve this issue because the moment is politically ripe," he said. "The further, I believe, we get away from Election Day – Nov. 6 of 2012 – the less urgency there will be, and the less likelihood of success."