"I think the prison reform bill has the biggest consensus of bipartisan support, so that ought to be the base bill. But other people have ideas, and they are entitled to offer them," Cornyn said, opening up the potential for changes to mandatory minimums or other, related provisions being attached as amendments.
Grassley has said that he is willing to have a conversation about mandatory minimums but that he has "a little different view than some other members have.
"The importation of heroin and cocaine isn't a major problem and ought to have high mandatory minimums, with the violence that comes from it?" Grassley asked. "They want to reduce that. I don't believe in that."
His own voting record indicates he is more amenable to Cornyn's bill, which was cosponsored in the last Congress by Democrat Sheldon Whitehouse. In fact, members say Grassley is looking forward to working on it.
"Senator Grassley has said he'd like to see it relatively soon, and so has Senator Cornyn," Whitehouse said. "Does that mean next week? I doubt it. Does that mean before the August recess? I very much think so."
Grassley has taken the helm of the Judiciary Committee just as the politics and attitudes surrounding criminal justice have shifted. The fallout from the 1988 presidential election, where the escape of inmate Willie Horton helped seal the victory for George H.W. Bush, is squarely in the rearview mirror, and even older-guard Republicans have changed their tune on the issue.
"I was one of those who early on, because judges were being too easy on some of these harsh criminals, did these mandatory sentences, but I think it's gone way too far," said Sen. Orrin Hatch, R-Utah.
Today, a new generation of Republicans sees reducing mandatory minimums for drug offenses and helping assimilate former prisoners back into society as a way to cut costs and make inroads with minority voters.
"We don't tell anyone they should do this for political reasons, but if good policy is good politics, then so be it," said Marc Levin, the policy director for Right on Crime, a conservative group pushing for criminal-justice reform legislation.
For budget-slashing Republicans, there is a practical urgency for reform. The federal prison population has ballooned from 25,000 inmates in 1980 to 219,000 in 2013. But without mandatory minimums being addressed, some advocates worry that justice reform may not make a substantial impact.
They warn that passing a bill aimed at reducing recidivism without accompanying legislation to reduce mandatory minimums won't do enough to cut prison costs or overcrowding. Today, drug offenders represent 42 percent of the population in federal prisons, and everyone from the Congressional Research Service to the Urban Institute believes that mandatory minimums are partly to blame.