Senate Majority Leader Harry Reid, D-Nev., speaks at the center for American Progress Action Fund in Washington, Monday, July 15, 2013. Reid spoke about ending the current gridlock in the Senate that according to him is harming the nation's ability to address key challenges. (AP Photo/Pablo Martinez Monsivais) Senate Majority Leader Harry Reid (D-Nev.) (Pablo Martinez Monsivais/AP)

Senate Majority Leader Harry Reid (D-Nev.) announced his support Tuesday for Sen. Kirsten Gillibrand's (D-N.Y.) bill to revamp how the military handles sexual assault cases, becoming the 50th public supporter of the measure.

Reid's support comes hours after his Nevada colleague, Sen. Dean Heller (R), became the bill's 49th public supporter.

Reid says he hopes to debate Gillibrand's bill and a less-far-reaching measure from Sen. Claire McCaskill (D-Mo.) on Wednesday. McCaskill's amendment is expected to pass, but Gillibrand's bill may struggle to get the 60 votes it will likely need to pass.

McCaskill does not support Gillibrand's proposal, believing it unwise to task attorneys far from the alleged assaults with determining innocence and guilt.

The issue doesn't break down neatly along partisan lines, as supporters of the military have been hesitant to take the power to investigate sexual assault cases away from military commanders, as Gillibrand's bill would do.

But a new poll from the Washington Post and ABC News shows nearly six in 10 Americans agree with the idea of handing that power to an independent group of military prosecutors.

Ed O'Keefe contributed to this report. Updated at 3:49 p.m.