Senate Judiciary Committee members grappled Thursday with the best strategy to overhaul the nation’s criminal justice system, since the leading bill has broad bipartisan support but the White House apparently backs only one part of it.

Chairman Charles E. Grassley of Iowa set a markup next week for a bill that represents a hard-negotiated compromise — first struck in 2015 — that backers say would pass the Senate with a bipartisan supermajority if brought to the floor. It is expected to easily advance from the committee and could be a signature legislative accomplishment for the Senate.

A broad and politically varied coalition of lawmakers and advocacy groups off Capitol Hill generally back the overhaul, which has two main components. One section aims to reduce sentences for nonviolent drug offenders, and the other aims to ease re-entry for prisoners.

But Majority Leader Mitch McConnell didn’t bring a version of the legislation to the floor in the last Congress because of opposition to the sentencing section from law enforcement groups and some Republican senators, Majority Whip John Cornyn of Texas told the committee Thursday. And now, President Donald Trump has voiced support only for the prison changes.

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Cornyn, the Senate’s No. 2 Republican leader, said, “I honestly don’t see a path forward” this year for the broader bipartisan bill.

“I’m worried that if we just revisit the Sentencing Reform and Corrections Act, which failed during the Obama administration, given this change in the new administration and its views on the sentencing reform component of it, we’re going to have nothing to show for our efforts,” said Cornyn, using the bill’s formal title. “I know we all tried to work together on this and it just didn’t work out.”

Instead, Cornyn said the committee’s best opportunity to move a criminal justice bill would be his legislation, proposed along with Republican Sen. Mike Lee of Utah and Democratic Sen. Sheldon Whitehouse of Rhode Island, which contains only provisions aimed at easing re-entry for prisoners — “and then building on that as we can” with an amendment process on the floor.

That process could include amendments on sentencing, based on a bill introduced in previous sessions by Lee and Democratic Whip Richard J. Durbin of Illinois.

Grassley responded that the compromise bill would be the best way to get the sentencing and prison provisions into law. The measure currently has 19 co-sponsors, and he said the backers are seeking more.

“It’s a matter of process and around here — nothing gets done unless it’s bipartisan,” Grassley said. “And I don’t often agree with Sen. Durbin, but we put together a bill that we worked really hard and we think it’s the only way of advancing both bills.”

Whitehouse said he would support both ways of moving forward since the sentencing bill was proposed five years ago, but that Cornyn’s strategy “actually might provide a more realistic way of getting this matter resolved.”

The Senate, however, could end up in the same place if the prison bill gets to the floor and then a supermajority of senators add the sentencing portion back in with an amendment, Whitehouse said.

“Waiting here for there to be the ultimate global concord to sort this out has yielded five years of nothing and I’m ready to go forward,” Whitehouse said.

Grassley countered, however, that there could still be senators who would block the prison bill from the floor if they knew there were more than 60 senators supporting a sentencing amendment. 

“That’s what we face,” Grassley said. “There’s some people around here [who] are just a little bit afraid of what you call an Assistant U.S. Attorneys Association and they’re stopping everything from being done that is so successful in the other states. When people are willing to stand up to those leaders of the Senate, we’ll get something done in both areas.”

Cornyn said he was just trying to find a way forward, “because we’re stuck.”