The committee-approved bill, S. 598, is titled the Respect for Marriage Act, and it would repeal language in DOMA that prevents the government from recognizing same-sex marriage. The Senate bill has 30 Democratic co-sponsors.

The bill has little chance of advancing in the Republican House, even if the full Senate were able to approve it. Still, House Judiciary Committee ranking member Jerrold Nadler (D-NY), who authored the repeal bill in the House, thanked his Senate counterparts and said public sentiment is shifting toward a desire to repeal DOMA.

"I wholeheartedly commend our allies in the Senate Judiciary Committee for voting today to repeal DOMA and send that ugly and discriminatory law into the history books, where it belongs," Nadler said. "I thank Chairman [Patrick] Leahy [(Vt.) and Senators Feinstein, [Kirsten] Gillibrand [(N.Y.)], [Charles] Schumer [(N.Y.)] and others for their important work in making history and getting us to this point. Clearly the tide is slowly but steadily turning toward equality and justice for all Americans."

According to committee Democrats, same-sex couples cannot file joint federal tax returns, receive spouse benefits under Social Security, or enjoy other federal rights under current law.

"DOMA was wrong when it passed in 1996 and it is wrong now," Feinstein said. "There are 131,000 legally married, same-sex couples in this country who are denied more than 1,100 federal rights and protections because of this discriminatory law."

Committee Chairman Patrick LeahyPatrick Joseph LeahyDem senator mocks Pruitt over alleged security threats: 'Nobody even knows who you are' Pruitt tells senators: ‘I share your concerns about some of these decisions’ Protesters hold up 'fire him' signs behind Pruitt during hearing MORE (D-Vt.) said it was wrong for the federal government to restrict these "highly personal freedoms and protections" only to opposite sex couples.

"The Federal Government should not deny recognition and protection to the thousands of Americans who are lawfully married under their state law," Leahy said. "We must repeal DOMA to ensure the freedom and equality of all of our citizens."