The Senate opened debate Tuesday on the annual Pentagon policy legislation with serious disagreements over reforms needed to address the growing problem of sexual assaults in the military.

The issue has virtually erased the usual partisan divides. Tea party favorite Sen. Rand Paul, R-Ky., is among those backing a proposal from Sen. Kirsten Gillibrand, D-N.Y., to change the way sexual assault cases are prosecuted by the military. Gillibrand's bill would take away from commanders the authority to decide who is prosecuted, leaving those decisions to outside independent prosecutors.

Gillibrand contends that the change would encourage more victims to speak up about their assaults, noting there were just 302 sexual assault prosecutions in 2012 even though a Pentagon study this year concluded that there were as many as 26,000 cases of unwanted sexual contact in the ranks.

"They must create an independent, unbiased military justice system that is deserving of the sacrifice that the men and women of the armed services make every single day," Gillibrand said.

The 2014 National Defense Authorization Act already includes a less controversial provision that would allow commanders to remain in the decision-making position, but would provide special legal aid to victims and make it a crime to retaliate against victims of assault.

Sen. Claire McCaskill, D-Mo., who is leading opposition to Gillibrand's proposal, argues that taking away from commanders the power to decide who is prosecuted could prevent those commanders from changing military culture and addressing the problem.

Sen. Kelly Ayotte, R-N.H., a McCaskill ally on the issue, spoke on the Senate floor about the need for commanders to step up and punish peers who don't address sexual assault.

"We [need to] have a climate in our military that says if you do not stop sexual assaults, prevent sexual assaults ... you will be relieved from command," Ayotte said.

Gillibrand says that a majority of senators support her proposal, which could get a vote as early as Tuesday. She needs 60 votes to advance the amendment.