Senate Judiciary Chairman Charles E. Grassley is leaning on his track record of processing judicial nominations to get a floor vote on a bipartisan bill he spearheaded to overhaul the nation’s criminal justice system.

In an unusual personal plea, the 85-year-old Iowa Republican on Thursday said he wanted “reciprocity” from Majority Leader Mitch McConnell for “what I’ve done in our unified effort on judges” during President Donald Trump’s administration.

Grassley has brushed aside or relaxed long-standing committee customs to get nominees to the floor quickly for final confirmation votes during Trump’s first two years in the White House, and McConnell made those a priority for floor time.

The dozen Trump appointments to the influential appeals courts — which have the final say in the vast majority of cases — was a record number for a president’s first year in office. Republicans now have confirmed 29 appeals court judges plus Supreme Court Justices Neil M. Gorsuch and Brett M. Kavanaugh during the Trump administration.

“I look at this in a very personal way,” Grassley told reporters. “Sen. McConnell and I have had a very close working relationship on judges. We’ve been very, very successful. And part of that success is because I’ve been able to get these nominees out of committee. We’ve made history, and we’ve got two good people on the Supreme Court.”

Grassley also said the new compromise bill is a chance for the first sentencing reform in a generation, is bipartisan, and got Trump’s backing Wednesday. “And it seems to me the Senate majority leader ought to be helping the president get his program through,” Grassley said.

But McConnell, who had at one point promised to do a whip count and bring the legislation to the floor if it had more than 60 votes, has said his caucus is split on the issue. He cast doubt Wednesday on whether he would allow a floor vote during the short lame-duck period, and spoke of other priorities.

And Majority Whip John Cornyn did the same Thursday, noting that he one senator can withhold consent for a floor vote and force a time-consuming process.

“I do think there are people in good faith who have some differences of opinion and they deserve to be heard as well,” Cornyn said during a committee hearing.

Sen. John Kennedy, a Judiciary Committee member who is critical of criminal justice changes in his home state of Louisiana, said that he would object to unanimous consent if the new federal bill went to the floor because there’s not enough time to do it right.

“I don’t think we’ll have the amount of time to get to it this year, not to do it properly, I just don’t,” Kennedy said. “We need to have a hearing. We need to know what we’re voting on. This is a very important issue and Americans are looking to us to get it right.”

Earlier Thursday, Sen. Tom Cotton, the Arkansas Republican who has been an outspoken opponent of the criminal justice overhaul, tweeted his concerns to Grassley in a way that made it appear he wouldn’t be agreeing to unanimous consent to move to the bill.

Grassley had also made a plea to other Republicans on the social media platform, writing Wednesday that, “I sincerely hope no GOP Sen is trying to undermine Pres Trump & son in law/adviser Kushner w false info on this TOUGH ON CRIME & SMART bill.”

Cotton replied: “agree, false info not helpful. Please release bill text to allow for full public discussion.” Cotton also tweeted that a Judiciary Committee hearing “would be helpful too.”

A few hours after Cotton’s tweet, the text of the bill was released. It combines prison measures to help federal prisoners better rejoin society with four sentencing provisions that would give judges more discretion as well as lower terms for crack cocaine, firearms and minor drug offenders, according to a summary distributed by the authors.

“This bill represents the culmination of a lot of hard work by lawmakers and advocates from across the political spectrum,” Grassley said. “President Trump has shown real leadership to advance these important reforms — the most significant in a generation. We have a real opportunity to make these important reforms a reality before the end of the year.”

Sen. Richard J. Durbin called it “the best chance in a generation to make meaningful changes in our federal drug sentencing laws.”

Joining the bill were Republican Sens. Mike Lee of Utah and Lindsey Graham of South Carolina, and Democratic Sens. Cory Booker of New Jersey and Sheldon Whitehouse of Rhode Island.

Cosponsors are Republican Sens. Tim Scott of South Carolina, Joni Ernst of Iowa, Jerry Moran of Kansas and Democratic Sens. Patrick J. Leahy of Vermont, Amy Klobuchar of Minnesota and Chris Coons of Delaware.

Correction: A previous version of this story incorrectly stated Cornyn’s position on the measure.