Senate Democrats and backers of gay marriage won a key victory Thursday in their quest to overturn the Defense of Marriage Act, but it’s unclear where it will go next.

The Senate Judiciary Committee voted 10-8 along party lines in favor for the Respect for Marriage Act, a bill sponsored by Sen. Dianne Feinstein (D-Calif.) that would repeal the Clinton-era law that defined marriage between a man and a woman.

“Because of DOMA, thousands of American families are now being treated unfairly by the federal government,” said Senate Judiciary Committee Chairman Patrick Leahy (D-Vt.). “This unfairness must end.”

Committee Republicans, noting that the bill faces bleak prospects for passing the full Congress, said the measure was a waste of time and the matter should be left up to the states. Six states – Iowa, New York, Connecticut, Vermont, Massachusetts and New Hampshire, as well as the District of Columbia – now recognize gay marriage.

Texas Sen. John Cornyn, chairman of the National Republican Senatorial Committee, argued that Senate Majority Leader Harry Reid (D-Nev.) would never bring such a controversial bill to the floor, particularly during the 2012 campaign cycle that could determine control of the Senate...