WASHINGTON -- The battle over how best to address sexual assault in the military hit a heated new pitch Thursday as Sen. Claire McCaskill (D-Mo.) said she would subject a competing proposal by Sen. Kirsten Gillibrand (D-N.Y.) to a filibuster vote.

McCaskill and Sen. Kelly Ayotte (R-N.H.) have offered a bill that would tweak reforms to the military justice system passed late last year, but would not go as far as Gillibrand's bill would by removing sexual assault cases from the military chain of command. Both measures are expected to come up before Congress takes its next break.

Gillibrand has said she backs McCaskill's bill and will vote to start debating it. If any senator chooses to filibuster a measure, it can take 60 votes to move a "motion to proceed" and start debate on that measure.

But McCaskill said Thursday she won't do the same for Gillibrand's bill and will insist on the filibuster threshold.

"No," McCaskill said when asked by reporters on Capitol Hill if she would vote to start debate. "There's a disagreement here. We do not believe that her bill will protect victims. We do not believe that it will result in more prosecutions. We do not believe it will increase reporting. And we believe there's real workability problems in terms of how quickly these cases will be brought to court."

"I think both bills will have to get 60 votes to proceed," McCaskill added. "We've got an awful lot of bills around here that had to get to 60 votes. I don't know why we would make an exception for this particular area, when we haven't made it for so many other areas that are of importance."

That view is somewhat ironic coming from McCaskill, who has complained about Republican filibusters in the past and voted last November to tighten the rules on some. She has also voted to limit filibusters on motions to proceed.

McCaskill's office said that a legitimate use of the filibuster against deeply controversial legislation is a completely separate issue from Republican abuse of the filibuster.

The heart of the dispute is whether the severe under-reporting of sexual assault in the military would be alleviated if cases were not run through the chain of command. Victims have said they often don't trust commanders and argued that removing such assaults from the chain of command would be the single best step to increase reporting. But McCaskill and Ayotte point to a recent report that found there was not enough evidence to show Gillibrand's proposal would improve matters. Gillibrand points to the Defense Department's Defense Advisory Committee on Women in the Services, which recommended unanimously that the New York senator's bill should be adopted.

Several advocates and victims of abuse in the military argued their case again Thursday in a press event with Gillibrand, Sen. Chuck Grassley (R-Iowa) and several other senators. One slammed the idea of filibustering the bill as cowardice.

"Using procedural tricks to block a bill that already has bipartisan, majority support in the Senate is an act of cowardice and breaks faith with the brave veterans who have suffered from a status quo in the military that is all too permissive of sexual assault," said Tom Tarantino, chief policy officer for the Iraq and Afghanistan Veterans of America.

Gillibrand, who had secured the support of a majority of her colleagues late last year but hadn't yet reached the 60 needed to break a filibuster, predicted she would prevail.

"Some say we can’t get 60 votes if needed to break a filibuster," Gillibrand said in another part of the Capitol shortly before McCaskill addressed reporters. "We disagree, because nowhere in America would we allow a boss to decide if an employee was sexually assaulted –- except the United States military."

Michael McAuliff covers Congress and politics for The Huffington Post. Talk to him on Facebook.