At least 51 votes are confirmed in the Senate for the Military Justice Improvement Act (MJIA), according to its author, Sen. Kirsten Gillibrand (D-NY).

“The majority of the Senate supports this bill, and 60 votes are within our sight,” Gillibrand said at a press conference Tuesday. She said she also has support from more senators than have officially signed on, and that she had plans to meet with all of her undecided colleagues. A vote on the MJIA, attached as an amendment to the 2014 defense spending bill, could come before Thanksgiving.

Three more senators have officially supported the bill in the last 24 hours, Sens. Harry Reid (D-NV), Cory Booker (D-NJ), and Dean Heller (D-NV). Senators supporting the MJIA released a new letter signed by 26 retired military personnel, including four retired generals or admirals speaking out for the first time. A social media campaign by the Service Women’s Action Network (SWAN) and other advocates to #PassMJIA has also helped fuel momentum for the bill this week.

Gillibrand’s renewed push comes on the heels of a new ABC News/Washington Post poll finding that six in ten Americans support letting independent prosecutors, rather than the chain of command, decide whether to prosecute cases of sexual assault and other serious non-military crimes.

The Pentagon has been strongly opposed to the MJIA, but as The Nation reported, military brass may be suppressing differing views on the issue. A senior officer said that if he came out in support of the measure, “It would kill my chances of ever having a good job again.”

Two female retired generals, Air Force Major General (Ret.) Martha Rainville and Brigadier General (Ret.) Loree Sutton, also spoke at Tuesday’s press conference, along with two sexual assault survivors and advocates.

“Far from ‘stripping’ commanders of accountability, as some detractors have suggested, these improvements will remove the inherent conflict of interest that clouds the perception and, all too often, the decision-making process under the current system,” Sutton said.

“Military leaders have made promises about addressing the problem of sexual assault for years and years, but the problem only seems to be getting worse. In fact, the current system seems to be part of the problem,” Sen. Chuck Grassley (R-IA) said.

Gillibrand said that the root problem is “the breach in trust” between assault survivors and the chain of command, and that now is not the time for more advisory panels. “We have boxes of advisory panel recommendations,” she said, including a recommendation from the Department of Defense’s own advisory committee on women in the military.