A bipartisan group of Senate lawmakers on Thursday unveiled a compromise proposal for criminal justice reform, in a bid to put the package back on track after conservative concerns sidelined it earlier this year.  

Senate Judiciary Committee Chairman Charles Grassley, R-Iowa, announced Thursday that they’d done some “fine-tuning” and claimed the new plan should address the concerns “in a bipartisan way.”

The legislation, which had been approved by the Senate Judiciary Committee last November, would allow some nonviolent drug offenders to get reduced prison sentences and give judges greater discretion in sentencing. The legislation had rare bipartisan support in the Senate and backing from President Obama, but it stalled earlier this year when some conservatives suggested that it could let violent offenders out of prison.

The reworked bill announced Thursday would still give judges discretion to give lesser sentences than federal mandatory minimums and eliminate mandatory life sentences for three-time, nonviolent drug offenders. It also would create programs to help prisoners successfully re-enter society.

But to address opponents' concerns about violent criminals, the new version would drop language that could have allowed reduced sentences for criminals who had possessed a firearm.

And in an effort to convince Senate Majority Leader Mitch McConnell, R-Ky., that there is strong Republican support, the sponsors also announced that they had picked up support from four additional GOP senators: Mark Kirk of Illinois, Dan Sullivan of Alaska, Thad Cochran of Mississippi and Steve Daines of Montana.

“There aren’t many comprehensive bills with this magnitude that have earned this kind of support,” Grassley said Thursday.

It was unclear if the changes would placate conservative critics, such as presidential candidate Ted Cruz, R-Texas, and Sen. Tom Cotton, R-Ark. Cotton has called it "a massive social experiment in criminal leniency."

Other conservatives, particularly former federal prosecutors like Sen. Jeff Sessions, R-Ala., have said they believe the bill could reverse an overall downward trend in crime.

Many of their Republican colleagues disagree.

In addition to Grassley, the bill is backed by Sen. John Cornyn, R-Texas, who long opposed any reductions in federal mandatory minimums but worked for years on the compromise bill. Illinois Sen. Dick Durbin, the No. 2 Democrat in the Senate, and Vermont Sen. Patrick Leahy, the top Democrat on the Judiciary Committee, also support the bill.

The aim of the legislation is to reduce overcrowding in the nation's prisons, save taxpayer dollars and give some nonviolent offenders a second chance while keeping the most dangerous criminals in prison. Disparate voices -- from Obama and the American Civil Liberties Union to the conservative Koch Industries -- have said the system is broken after years of "tough-on-crime" laws and have backed the Senate bill.

In 1980, the federal prison population was less than 25,000. Today, it is more than 200,000.

The House Judiciary Committee has approved several separate criminal justice bills, with the eventual goal of moving them separately or together on the House floor. Unlike McConnell, House Speaker Paul Ryan, R-Wis., has said the legislation is a priority. But he hasn't given a timeline for when it will move.

After conservatives balked, both Cornyn and House Majority Leader Kevin McCarthy, R-Calif., conceded that the legislation doesn't have to move this year. But supporters have acknowledged that Obama's strong support could be beneficial. 

The Associated Press contributed to this report.