A disparate group of senators took to the podium Tuesday to support a renewed push by Sen. Kirsten Gillibrand, D-N.Y., to overhaul the military's legal procedures regarding sexual assault.

Flanked by Sens. Susan Collins, R-Maine; Rand Paul, R-Ky.; Ted Cruz, R-Texas; Barbara Boxer, D-Calif.; Richard Blumenthal, D-Conn., and others, Gillibrand urged congressional leaders to include her Military Justice Improvement bill as a rider to the defense bill unveiled Tuesdayday.

The bill proposes to strip some commanders of the authority to decide whether to prosecute a sexual assault case.

Gillibrand said with the defense bill pending and a report due this week from the Defense Department to President Obama on military sexual assault, the time has come for reform.

"No more calls for just 'some more time.' The DoD has failed on this issue for 20 years," Gillibrand said during a press conference at the U.S. Capitol on Tuesday.

Gillibrand's bill would eliminate a provision from the Uniform Code of Military Justice that lets some senior commanders decide whether to prosecute a crime.

The bill would give that decision-making authority to military prosecutors on crimes punishable by a year or more in jail — with the exception of 37 crimes unique to the military, such as disobeying direct orders or taking unauthorized absence.

Citing an article in the New York Times Magazine on Sunday on the case of Air Force Lt. Col. James Wilkerson, who was convicted of sexually assaulting a civilian woman but later was released from prison and reinstated at rank by a general officer with decision authority, Gillibrand said other recent sexual assault cases show that changes implemented a year ago aren't working.

"The scandals of the last 12 months show they still don't get it. Congress should vote ... our service members deserve it," Gillibrand said.

The proposed measure is similar to legislation introduced by Gillibrand earlier this year that fell five votes shy of passage.

In March, Congress did pass a bill addressing the issue of military sexual assault prosecution — legislation sponsored by Sen. Claire McCaskill, D-Mo., that made changes, including eliminating the "good soldier" legal defense from evidence rules in some cases and giving victims more control over how their cases are prosecuted and handled.

In a blog post on Huffington Post on Tuesday, McCaskill said she will be reading the DoD report this week to determine whether reporting of sexual crimes is increasing, if incidents are decreasing and what troops think of the system.

"Even if this week's report shows the progress we're hoping for, it's sure to also demonstrate areas where we need to continue working — and as we look at those areas, we must ensure the remedies we propose address the problems that exist," McCaskill said.

Citing figures that showed the number of reports of sexual assault in the military increased from 3,400 to 5,061 in 2013 but the number of unrestricted reports — those filed which allow for prosecution — declined, Gillibrand said she will push for a vote on the stand-alone bill, and if necessary, press the president for action.

"It's very possible the president could fix this himself," Gillibrand said.

Air Force Col. Don Christensen, former chief prosecutor of the United States Air Force and attorney on the Wilkerson case, said the president "has ultimate authority" but that the "cleanest way" for the president to change the UCMJ would be to support the "Gillibrand bill and get it passed."

Calling attention to the bill's co-sponsors, who include politicians at polar opposites of the political spectrum, Boxer said Congress needs to act because the military "is not serious about cracking down on sexual assault."

"This is an unusual coalition. I hope you note that because it speaks to an issue of heart and it brings us together," Boxer said.