A diverse coalition of senators, led by New York Democrat Kirsten Gillibrand, touted new support Tuesday for a proposal to change how the military prosecutes sexual assault cases.

Tea Party conservative Sen. Rand Paul, R-Ky., announced his support for Gillibrand’s proposal to curb military sexual violence, breathing new life into an initiative that stalled after the Senate Armed Services Committee rejected it earlier this year.

“I try not to look at issues from a partisan view. … I’m concerned that victims of assault will be deterred from reporting their assault if they have to report it to their boss,” Paul said at a Monday press conference, standing with Sens. Chuck Grassley, R-Iowa, Ted Cruz, R-Texas, Mazie Hirono, D-Hawaii, Barbara Boxer, D-Calif., Richard Blumenthal, D-Conn.,and Gillibrand.

Gillibrand’s legislation would remove the military chain of command from the decision of whether or not to prosecute an allegation of sexual assault.

“[Victims] don’t trust the chain of command. If the victims do not trust the chain of command, they will not report these cases. … They will not trust the system that the chain of command has put in place,” Gillibrand said.

Paul said that he indicated his support for the proposal after a personal discussion with Gillibrand, who agreed to make minor changes to the legislation.

“I see no reason why conservatives shouldn’t support this," the Kentucky Republican told reporters. "Only thing standing in the way is the status quo.”

The issue of military criminal justice slices across party lines. The 17 senators on the Armed Services Committee who rejected Gillibrand’s proposal earlier included Republicans and Democrats and the coalition that supports it is equally bipartisan.

So even with this newest show of strength, the proposal faces serious obstacles. There is no demonstrated appetite for it in the Republican-controlled House. Senior Democrats on the Armed Services Committee, including Sens. Carl Levin, D-Mich., and Claire McCaskill, D-Mo., support an alternative. And the Pentagon strenuously objects to it on the grounds that commanders need to maintain their authority if they are to change military culture to reduce sexual violence.

Critics of the bill support the Pentagon’s argument. Levin and McCaskill led an effort in June to ensure that cases the chain of command chose not to prosecute would be reviewed by the next-highst commander in the chain. This was eventually adopted by the Armed Services Committee.