With a markup set to begin Thursday, the Senate Judiciary Committee is expected to approve legislation to repeal the Defense of Marriage Act, but with little chance of passage in the full Senate, the measure has become largely a base-rallying message for the two parties.

“It probably won’t move forward on the floor, but I do think we’ll have a favorable outcome with the committee markup, and it will be an opportunity to keep building co-sponsors and keep building support in the Senate on this issue,” said Brian Moulton, chief legislative counsel with the Human Rights Campaign.

The panel will begin marking up the Respect for Marriage Act, which has 30 co-sponsors in the Senate and would repeal DOMA, the 1996 law that defines marriage as between one man and one woman. The measure is likely to be voted on next week.

All 10 Democrats on the committee back the bill, including Sen. Dianne Feinstein (Calif.), who introduced the measure in March. Feinstein is a former mayor of San Francisco and a longtime champion for gay rights.

Judiciary Chairman Patrick Leahy (D-Vt.) has also pushed for gay rights, which he believes is a continuation of the nation’s fight for civil rights.

“If we don’t bring these issues up, if we don’t bring them up and have votes, then nothing ever happens,” Leahy said Friday on Vermont Public Radio. “Back when I was a kid in high school and college, people would say, ‘We really can’t bring up any good civil rights laws because the southerners would block them, or they won’t pass.’… Fortunately, some brave people started bringing them up, and after a while, they passed.”

At a July hearing on DOMA, Leahy said some GOP Members did not attend and few questions were asked, which he attributed to a softening opposition. He added that some Republicans have told him privately that they were “not quite ready, but sooner or later this is going to pass.”

Senate Judiciary ranking member Chuck Grassley (R-Iowa) believes the bill is unnecessary and said the will of the Senate was carried out when DOMA was passed, 85-14, in 1996. A spokeswoman pointed to his opening statement at the hearing in July.

“George Orwell would have marveled at that name. A real bill to restore marriage would restore marriage as it has been known: as between one man and one woman,” Grassley said. “That is the view of marriage that I support. This bill would undermine, not restore, marriage by repealing the Defense of Marriage Act.”

“The repeal of DOMA will likely end in the Judiciary Committee,” a Republican aide said. “The Senate isn’t going to pass the bill. Even Sen. Feinstein has admitted the votes aren’t there, and the House probably won’t even consider the bill. It’s a political messaging bill for the liberal base.”

But supporters remain unbowed. “I don’t expect we’d be able to get to 60 [votes to defeat a filibuster] on the Senate floor,” Moulton said. But he added that the markup will allow advocates to keep the matter moving forward.

“Certainly we are still continuing to build co-sponsors on the bill, to educate; it’s the first Congress where we have had a repeal bill in the Senate at all,” Moulton continued.

Moulton said that moving forward in the Judiciary Committee also allows Democrats “to show their leadership” on the issue, which the HRC argues is good politics as the issue wins more acceptance.

“We’ve seen majorities of Americans now supporting not only marriage equality but specifically supporting the repeal of DOMA, so I do think they are bringing up an issue that has popular support and will help raise the profile of what’s going on and the rights and benefits that are being denied to lawfully married same-sex couples.”

President Barack Obama in February announced that the administration would no longer defend DOMA in court. The move prompted Feinstein to introduce her bill in March.

Speaker John Boehner (R-Ohio), who opposed Obama’s decision, subsequently enlisted former Solicitor General Paul Clement to defend DOMA on behalf of the House’s Bipartisan Legal Advisory Group.