A proposal to establish an aggressive new system to prosecute sex cases in the military has picked up two key Republican backers as proponents continue seeking enough support to force a vote on the plan in the coming weeks.

Sens. Rand Paul (R-Ky.) and Ted Cruz (R-Tex.) said Tuesday that they now fully support a proposal by Sen. Kirsten Gillibrand (D-N.Y.) that would limit a military commander’s ability to oversee investigations and prosecutions of alleged sexual assaults in their units.

Military commanders strongly oppose the idea, saying it would jeopardize the chain of command and the cohesion of units in the field. The Senate Armed Services Committee rejected the Gillibrand proposal last month as it put the finishing touches on its version of the National Defense Authorization Act. But the panel approved other proposals by senators of both parties to clarify how the military should investigate allegations of sexual assault and to stiffen penalties for service members convicted of such crimes.

Gillibrand has pressed ahead in recent weeks to secure the support of at least 51 senators to hold a vote on her plan when the Senate begins debating the defense bill in the coming days. As of Tuesday, she said she has commitments from at least 34.

“This is not a Democratic idea. It is not a Republican idea. It is a good idea that meets the needs of the victims, creates transparency and accountability, and creates the needed objectivity that this issue deserves,” Gillibrand said at a Tuesday news conference.

Gillibrand was flanked by Paul and Cruz and party stalwarts, including Sens. Charles E. Grassley (R-Iowa) and Barbara Boxer (D-Calif.), as well as newer colleagues, including Sens. Richard Blumenthal (D-Conn.) and Mazie Hirono (D-Hawaii). It was a notable bipartisan event that started at almost the same moment that Senate leaders were announcing a tentative deal to avert a showdown over Senate rules and the use of the filibuster to block presidential nominations.

The backing of Paul and Cruz is critical, according to aides of supportive senators, who said that the pair will help attract more attention for the issue in conservative circles and persuade other GOP senators to back the plan. The collaboration of Paul, Cruz and Gillibrand, relatively young and ambitious senators, is also notable as all are often mentioned as future presidential candidates, and thus future potential commanders in chief.

“When I heard about this, my first impression was a positive one,” Paul said in explaining his support, adding that he asked Gillibrand to tweak her proposal so that it focused only on how military prosecutors would handle major crimes such assault and murder. With those changes, “I see no reason why conservatives shouldn’t support this,” Paul said.

Cruz, who is the most junior member of the Armed Services Committee, said he had been undecided on Gillibrand’s proposal when the panel debated it, but he credited her “exceptionally passionate and able advocacy” for convincing him.

“I think all of us, Republicans, Democrats, and I think also the commanders in the military, want to solve this problem,” Cruz said.

Grassley and Boxer said they have served long enough in Congress to know that sexual assault has been a pervasive issue in the military.

Boxer used a series of charts to highlight statements by Defense Secretary Chuck Hagel and his six immediate predecessors, all of whom said at one time that they had either “zero tolerance” or “no tolerance” for sexual assault in the ranks.

“It’s enough with the words. It’s enough with the empty promises. It’s time for some real change,” Boxer said.

It is unclear whether Gillibrand and her colleagues will be able to secure at least 51 votes for their plan. Debate on the defense bill could begin as early as next week.

Sen. Carl Levin (D-Mich.), chairman of the Armed Services Committee, is among those who oppose the plan but said Tuesday that if Gillibrand garners enough support, “we’ll have a debate.”

After her news conference, Gillibrand was seen lobbying Sens. Daniel Coats (R-Ind.) and Jon Tester (D-Mont.) in hopes of earning their support.