"I see no reason why conservatives shouldn't support this," Sen. Rand Paul, R-Texas, said at a news conference with Gillibrand, D-N.Y., Sen. Ted Cruz, R-Texas, and other senators from both sides of the aisle.
"The only thing I think is standing in the way is, just sort of the status quo," Paul said.
Besides Paul and Cruz, Republican senators joining Gillibrand in promoting the proposed Military Justice Improvement Act included Charles Grassley of Iowa, Lisa Murkowski of Alaska and Susan Collins of Maine.
They are part of a bipartisan group of 33 senators -- including Sens. Tom Udall, D-N.M., Mary Landrieu, D-La., and Ed Markey, D-Mass., who was sworn in Tuesday -- promoting Gillibrand's bill, which will be offered as an amendment to the annual defense-budget authorization bill as early as next week.
Gillibrand's proposal would give military prosecutors rather than commanders the power to decide which sexual assaults to try. The goal is to increase the number of people who report cases without fear of retaliation.
"If the victims do not trust the chain of command, they will not report these cases," Gillibrand told reporters.
"If they have witnessed other people reporting being retaliated against, if they've witnessed others being shoved out of the military because they reported these crimes, they will not trust the system that the chain of command has put into place," she said.
"There can be no prosecution, there can be no deterrence, if we don't have reporting of crimes," said Cruz, who, like Paul, has been discussed within the party as a possible 2016 presidential hopeful.
"The status quo is out of the mainstream," said Sen. Barbara Boxer, D-Calif. "It isn't working and I am as proud as I can be to stand with a coalition like this."
Despite bipartisan support, Gillibrand's measure was defeated at the Senate committee level.
The Armed Services Committee got behind a more modest provision pushed by committee Chairman Carl Levin, D-Mich.
Levin's bill would require a senior military officer to review decisions by commanders who decline to prosecute sexual assault cases. This would be a change from current practice, but it would keep prosecution of such cases within the chain of command, as the military wants.
Levin defended his approach at a breakfast with reporters Tuesday.
"You've got to hold commanders accountable for changing the culture," Gannett News Service quoted him as saying.
The Pentagon estimated in May 26,000 military members experienced "unwanted sexual contact" last year, up from 2011's 19,000 cases.
Yet only a fraction of that number -- 3,374 -- filed sexual-assault reports with military police or prosecutors, the annual Pentagon report said.
Defense officials say most victims don't press charges because they fear retaliation or banishment from their units.
Notable deaths of 2014 [PHOTOS]