They may not have the votes for passage, but Senate Democrats say they aren’t giving up on their push to repeal the Defense of Marriage Act.

“No, I don’t believe it does at this stage,” Sen. Dianne Feinstein (D-Calif.) said when asked whether her legislation to repeal the 1996 law that defines marriage as between one man and one woman has 60 votes in the Senate.

But she insisted that next month’s Judiciary Committee markup of the bill is important to build momentum for repeal and said it is likely to be approved by the committee.

“Look, some battles take 10 years, some take five, some take two, it all depends,” she said. “We’re in it for the long haul, and it could go on for years. I’m not clairvoyant. I don’t know. I do know it’s the right thing to do.”

For Democrats and Republicans, DOMA has become a flash point in the culture wars this year, after it became gay rights activists’ top priority following last year’s repeal of “don’t ask, don’t tell,” the policy that prohibited gay individuals from openly serving in the military. In February, President Barack Obama said DOMA was unconstitutional and instructed the Justice Department not to defend it in court. Speaker John Boehner (R-Ohio), following a party-line vote by the Bipartisan Legal Advisory Group, took steps to defend the law in court cases and criticized the White House for no longer doing so.

At this month’s 2011 Values Voter Summit, the Speaker pledged to the gathering of conservative activists that, “If the Justice Department isn’t going to defend this act passed by Congress, then we will.”

Despite the back-and-forth, a repeal of DOMA is unlikely this year and could be an even more difficult legislative task than last year’s successful vote to repeal “don’t ask, don’t tell.”

“In terms of a legislative strategy, what they’re having to deal with is the political reality that this isn’t going to happen,” a Democratic strategist said. “We were able to get [the] ‘don’t ask, don’t tell’ [repeal] through because people had a fairly lengthy discussion of the issue and we had both chambers. But now, even if we were able to get it through the Senate, we can’t get it through the House. So let’s focus on the things we can find agreement on.”

Activists also acknowledge the path to overturning DOMA could be long. And while they are just as pessimistic about the chances for Feinstein’s bill this year, they maintain that the legislative push is still necessary.

“I think if you look back at the trajectory of ‘don’t ask, don’t tell’ repeal, the first bill dated back to 2005,” said Zeke Stokes, a spokesman for the Servicemembers Legal Defense Network. “Building the same kind of public support is critical to getting DOMA repeal done.”

Feinstein’s bill has 30 co-sponsors, but absent from the list are vulnerable incumbents up for re-election next year. As one GOP leadership aide suggested, “I don’t think people like Sen. [Claire] McCaskill [D-Mo.] want to have to vote on this bill.”

And while eight Republicans crossed party lines to vote in favor of the DADT repeal last year, it’s unclear whether any of them would do the same to overturn DOMA. Two of those Republicans, Sens. John Ensign (Nev.) and George Voinovich (Ohio), are no longer serving, and others, including Sen. Susan Collins (Maine), maintain that gay marriage is a state issue.

Collins’ lack of support is significant because she was the lone Republican to vote for the DADT repeal in committee last year and helped lead the charge for the successful Senate vote, along with Sen. Joe Lieberman (I-Conn.). The White House tapped Lieberman to carry the effort on the Senate side, betting he would be able to court a handful of GOP moderates to ensure that the bill had 60 votes to pass on the floor.

There has been no similar strategy to shepherd a legislative repeal of DOMA through Congress, although Obama has publicly endorsed Feinstein’s legislation, which has a companion bill sponsored by Rep. Jerrold Nadler (D-N.Y.) in the House.

Obama heartened the gay community in February when he said DOMA was unconstitutional. He touched on the issue at the Human Rights Campaign’s annual dinner earlier this month. At that event, Obama assured the crowd, “We’re making real and lasting change.

“We can be proud of the progress we’ve already made,” he said. “And I’m going to continue to fight alongside you.”

Obama’s public push rallies a base important to his re-election efforts, and any kind of legislative action, regardless of its chances, helps build on that message, the argument goes.

While Democratic aides have grumbled all year about Obama’s muddled message on jobs and the economy, they nevertheless maintain that the fight on DOMA is helpful to the party.

“Unfortunately, I don’t see the Senate making a great deal of progress on jobs one way or the other,” Nadler said in a phone interview. “The House isn’t either, [so] I don’t think it’s a distraction. I think this government needs to do more than one thing at a time.”