Updated: 9:42 p.m.

Gay rights groups are injecting new urgency into their push to pass a repeal of the military’s ban on openly gay service members in the lame-duck session as a prominent Senate Republican steps up his efforts to nix the vote.

Aubrey Sarvis, executive director of the Servicemembers Legal Defense Network, delivered a panicked message to supporters Monday, calling attention to the short window of time for shaping the debate on the “don’t ask, don’t tell” policy. Some Senate Democrats are aiming for a vote on the annual defense authorization during the lame duck, which begins next week, and the bill could include the repeal language.

“The next 12 to 36 hours are critical to repeal of ‘Don’t Ask’; important conversations on moving the defense bill are happening now,” Sarvis wrote in the e-mail.

The e-mail comes as Senate Armed Services Chairman Carl Levin (D-Mich.) and ranking member John McCain (R-Ariz.) discuss whether to include the repeal in the defense authorization bill. McCain, the most vocal Senate critic of a repeal, has threatened to filibuster the bill if it includes the provision.

White House Communications Director Dan Pfeiffer said in an e-mail Monday night that President Barack Obama “opposes any effort to strip” the provision from the bill. The House has already passed a defense authorization that includes the repeal.

Sarvis told Roll Call that he expects Levin to bring the defense bill to a vote with the repeal in it, and he called it “premature” to speculate on whether Levin will yield to McCain’s pressure. The most important thing for now, he said, is for proponents of the repeal to take the reins in framing the message on the issue.

“There’s no doubt McCain is trying to frame the debate early, even before Senators return for the lame duck,” Sarvis said. “We’re trying to counter where McCain is out there saying the only bill that can move out there is a watered-down bill. That assertion needs to be pushed back on.”

Sarvis said his organization will focus much of its lobbying on a handful of GOP Senators who may help to overcome a filibuster by McCain. They include Sens. Olympia Snowe (Maine), Susan Collins (Maine), George Voinovich (Ohio), Scott Brown (Mass.) and Dick Lugar (Ind.).

The Human Rights Campaign launched an initiative Monday that targets Senators in Alaska, Arkansas, Illinois, Indiana, Maine, Ohio, Virginia and West Virginia with phone calls, letters to the editor and print advertisements aimed at building support for passing the “don’t ask” repeal during the lame-duck session.

The Pentagon is scheduled to release on Dec. 1 a yearlong study on the effects of a repeal, and supporters of the repeal are expecting a positive review that could give political cover to Republicans who are deciding their stance. Obama and Defense Secretary Robert Gates also recently called on Congress to pass the repeal this year.

But some repeal proponents fear that Levin may ultimately comply with McCain in order to advance the defense authorization. Republicans, along with a handful of conservative Democrats, have already blocked the bill from coming to the floor twice.

McCain spokeswoman Brooke Buchanan said the Arizona Republican “continues to have discussions” with Levin and that he remains opposed to keeping the repeal in the bill.

Further complicating the matter is the possibility that Senate Majority Leader Harry Reid (D-Nev.) may also try to attach an immigration proposal known as the DREAM Act to the authorization. The measure is aimed at giving illegal-immigrant children a path to citizenship if they go to college or join the military.

Last week, when his re-election campaign was in jeopardy, Reid vowed during a Univision interview to tie the provision to the authorization during the lame duck. But when he made the same move in September, the bill went down, along with it a vote on the “don’t ask” repeal.

“The last time we had this vote, the thing that stopped it was not ‘don’t ask, don’t tell,’” said Christopher Barron of GOProud, a gay rights organization for conservatives.

“If Sen. Levin wants to be the first chairman to avoid not passing a defense bill in 50 years, he doesn’t need to jettison ‘don’t ask, don’t tell.’ He needs to guarantee that the DREAM Act will not be a part of this,” Barron added.

At least one immigration rights group is giving Reid some wiggle room on how he plans to carry out his promise to Latinos. “Let’s wait for the big guns to sit down and make some decisions,” said Frank Sharry, executive director of America’s Voice.

“Right now, the Senate Majority Leader promised, he delivered on that promise in September, he just got re-elected,” Sharry said. “We’ll take it from there.”