Sen. Kirsten Gillibrand, D-N.Y., has been promised a vote on her bill to remove the prosecution of violent crime in the military from the chain of command, but when that vote will happen remains unclear.

Leaders, opponents and supporters of the bill all would like to have a vote on Gillibrand’s legislation, as well as related bills, as soon as possible. But aides point to a procedural bottleneck, with must-pass bills like the budget agreement and the larger defense package still on the docket as the winter holidays quickly approach.

Plus, Republicans, still sore from Majority Leader Harry Reid’s move to change the Senate’s procedural rules, are unlikely to consent to proceeding on any issue without employing time-consuming procedural maneuvers.

And unlike the Senate minority leader and other disgruntled Republicans — and armed with an assurance for a future vote —  Gillibrand has no plans to stop the overall defense bill to secure a roll call now. As it stands, she doesn’t have the 60 votes she needs and would not gain from further upsetting Sen. Carl Levin, D-Mich., the chairman of the Armed Services Committee on which she serves.

“I have an assurance that we will get a vote just not when we will have a vote,” Gillibrand said this week of her legislation, which will be put on the official Senate calendar. “But my goal is to get a vote right away and the reason is, is the men and women who have survived these atrocities have taken so much time at great personal expense to be here, to tell their stories, and I think they deserve a vote. So I’d like to get a vote sooner than later but I will work with the majority leader to find a time that fits in the schedule.”

Gillibrand has plateaued at 53 public supporters of her bill, though she claims to have more “yes” votes than have been declared and continues to speak with undecided senators.

“The more time we have, those stories can be told and the undecided senators can get more information about what people will really think,” the New York Democrat said.

Levin, however, might not agree with such a characterization. The chairman pushed back when asked if he thought delaying the sexual assault debate until 2014 would deflate Gillibrand’s momentum.

“You’re assuming that there’s momentum,” he said. “I don’t want to agree with your assumption.”

Levin said on Tuesday he was encouraging Reid to hold votes before Christmas on both the Gillibrand proposal and a package introduced by Sen. Claire McCaskill, D-Mo.

McCaskill and Republican Kelly Ayotte of New Hampshire supported the sexual-assault changes included in the bicameral, bipartisan defense authorization agreement.

“This agreement represents a huge win for justice in America’s Armed Forces. While we’re frustrated that votes on additional measures did not occur, these historic reforms — including installing civilian review over prosecutorial decisions, barring commanders from changing jury verdicts, assigning victims their own legal counsel, criminalizing retaliation against victims, and mandating dishonorable discharge for convicted sex offenders — will mean a new day for justice for American servicemembers. And we’re going to work as hard as we can to enact these critical reforms into law,” the duo said in a statement.

At this point, the biggest obstacles leaders face in trying to wrap work on the defense authorization bill — which has passed each year for more than a half-century — are senators upset about a lack of debate on amendments and those who would like to see tougher sanctions imposed on Iran.