Senators involved in the talks say the potential changes are meant to address concerns from the GOP caucus. A small but vocal wing remain adamantly opposed to the legislation, and several others have said they are wary about the impacts of the bill, lowering the prospects of passing it before the end of the year.

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"I think all I should say is that we're taking into consideration the concerns that a lot of members in our conference had, the ones who are undecided, and we're seeing what we can do to accommodate them and getting more cosponsors," Grassley said on Thursday.

"We're discussing it in terms of how to increase the number of votes for it. There are lots of people with ideas about how to increase Republican votes but usually at the expensive of Democratic votes," he said. "It's a very delicate balance. It's a tricky equation."

Changes to the legislation could make it harder for senators to get the measure to Trump's desk before 2019. Senators have 10 session days before they are scheduled to leave for the year. During that time they're expected to tackle a Dec. 7 government funding bill, a farm bill and a debate on U.S.-Saudi relations.

Trump threw his support behind the Senate's criminal justice bill earlier this month, touting it as "tough on crime." The legislation would take a House-passed prison reform bill and add in four changes to sentencing laws, including lowering mandatory minimums for some drug-related felonies and retroactively applying the 2010 Fair Sentencing Act.

An administration official told The Hill that the White House asked GOP sponsors of the legislation to make changes addressing law enforcement concerns and, in turn, win over some of the more skeptical Republicans.

Grassley denied Thursday that the White House asked for changes to the bill.

One potential change would be to add the list of crimes that would exclude an individual from "earned time" credits that allow an inmate to take days off their sentence for completing certain programs or activities.

Asked if Cotton and others were using the potential changes as pretense for stalling the bill, Durbin quipped, "that would question the motive of a colleague."

Conservatives have seized on opposition to the bill from the National Sheriffs' Association, which warned in a Nov. 15 letter to Senate leadership that the legislation amounted to a "social experiment."

A bipartisan group of senators supporting a-backed criminal justice bill is discussing changes to the legislation as they try to win over more Republicans."The current draft of the First Step legislation remains troubling to the leaders of law enforcement," the group wrote