The Senate’s sweeping overhaul of the criminal justice system cleared a major hurdle Monday, with an overwhelming majority helping to advance what probably will be one of President Trump’s final bipartisan accomplishments from his first two years in office. 

Senators voted 82 to 12 to end debate on the First Step Act and steer the legislation to a final vote, probably scheduled for Tuesday.

The bill would revise several sentencing laws, such as reducing the “three strikes” penalty for drug felonies from life behind bars to 25 years and retroactively limiting the disparity in sentencing guidelines between crack and powder cocaine offenses. The latter would affect about 2,000 current federal inmates. 

It also overhauls the federal prison system to help inmates earn reduced sentences and lower recidivism rates. A different version passed the House this year, so the House would have to pass the latest draft before it can be sent to Trump for his signature. 

The bill, which would not cover state jails and prisons, would reduce the federal inmate population by about 53,000 people in one year, according to the Congressional Budget Office. There were about 181,000 federal inmates as of Dec. 13, according to the Bureau of Prisons. 

During Senate debate, Majority Whip John Cornyn (R-Tex.) acknowledged a reality — the fear among politicians of being labeled “soft on crime.” He said the bipartisan legislation is “about being smart on crime and getting the best results.”

Cornyn said there are inmates “who understand they made a mistake and paid their debt to society and want to turn their lives around.”

Before a final Senate vote, dozens of the bill’s proponents will have to defeat “legislative poison pills” that they say are designed to kill the bipartisan compromise that has been carefully negotiated among Democratic and GOP lawmakers, as well as the Trump administration. 

Sens. Tom Cotton (R-Ark.) and John Neely Kennedy (R-La.) will get a vote on an amendment that would bar people convicted of various offenses, including certain sex crimes, from being able to qualify for reduced sentences. The legislation has a number of exclusions, but Cotton and Kennedy want to add more crimes, such as coercing a minor for sexual activity, to the list. GOP Sens. Patrick J. Toomey (Pa.), Jon Kyl (Ariz.) and John Barrasso (Wyo.) have endorsed Cotton and Kennedy’s effort, suggesting that they, too, are uncomfortable with the underlying bill. 

Procedurally, their amendment would need only a simple majority to pass, so some Republicans will have to band with Democratic senators to kill it. And senators who wrote the bill say there are safeguards meant to prevent violent criminals from being prematurely released. 

“From the standpoint that they aren’t specifically mentioned, the answer is, that’s true, they aren’t,” said Senate Judiciary Committee Chairman Charles E. Grassley (R-Iowa). But “the reasons they aren’t is because we think that other parts of the law covers it and also the process that somebody has to go through to get a review of their sentence, the prosecutors’ got to go through that as well.” 

Democrats had pushed for a more generous bill, and similar yet more expansive legislation under the Obama administration was scuttled by Republicans. But most if not all Democratic senators are expected to support the First Step Act — even as they emphasize that the bill alone is far from enough. 

“It is a compromise of a compromise,” Sen. Kamala D. Harris (D-Calif.) said in a statement Monday announcing her support for the bill. “We ultimately need to make far greater reforms if we are to right the wrongs that exist in our criminal justice system.”