Michigan Senator Carl Levin on Thursday became the 31st co-sponsor of a bill that would repeal the Defense of Marriage Act (DOMA), the 1996 law that bars federal agencies and the military from recognizing the legal marriages of gay and lesbian couples, gay weekly The Washington Blade reported.

Levin's endorsement comes just weeks before the measure is expected to clear the Senate Judiciary Committee.

But while passage in the Democrat-controlled Senate is looking brighter, the issue is a non-starter in the Republican-controlled House, whose speaker, John Boehner, is defending the law in court.

(Related: John Boehner criticizes Obama's gay marriage decision.)

The California-based gay rights group the Courage Campaign has been lobbying senators to back the measure, which was first introduced in 2009 by New York Rep. Jerrold Nadler. California Senator Dianne Feinstein introduced the bill in the Senate.

“Carl Levin is in many ways the conscience of the Senate,” said Rick Jacobs, chair of the Courage Campaign. “As a leader in defense and national security issues, Sen. Levin understands that America's true power comes from its diverse population. That's why his support for Sen. Feinstein's bill to repeal the Defense of Marriage Act means so such. American soldiers can now bear arms without hiding that they are gay and lesbian; when they come home, their marriages deserve to be treated equally.”

Last month, Florida Rep. Ileana Ros-Lehtinen came under heavy fire from social conservatives when she became the first Republican to co-sponsor the proposed legislation.