Senate Democrats’ efforts to overturn the Defense of Marriage Act (DOMA), took a procedural step forward today - but final passage into law faces a very uphill climb.

By a party-line vote of 10-8, the Senate Judiciary Committee passed the repeal of DOMA, the Clinton administration law that defines marriage as a union between a man and a union, out of committee by voting for the Respect for Marriage Act bill.

“So we begin with a single step on a march to equality,” committee chairman  Sen. Patrick Leahy, D-Vt., said at a news conference following the vote. “Marriage is a matter for the states to determine — whether it’s my state or any other state. And those Americans who are lawfully married should have the same protection under federal laws that my wife and I enjoy.”

While noting disappointment at not having a single Republican vote in the committee, Sen. Dianne Feinstein, D-Calif., hailed the procedural step.

“DOMA is discriminatory,” Feinstein said. “DOMA prevents people legally married in a state to get the same rights and benefits — federal rights and benefits that a heterosexual couple would get. So it treats one class differently from another class.”

The bill’s next step is to be sent to the full Senate for consideration. It’s unclear when, if at all, the majority leader will take up the bill in front of the full Senate.

If taken up, prospects for final passage in the Senate are bleak. They look even bleaker in the Republican-controlled House of Representatives.

“Marriage equality will pass,” said Sen. Charles Schumer, D-N.Y. “The question is not if, but when. And we should just go forward and do it. … We know we’re on the side of history, and we know that this will happen. And we just hope it’s sooner, not later.”