(CNN) Senate Majority Leader Mitch McConnell faces a tough choice: whether to put up for a vote a major criminal justice reform bill over the opposition of some hard-charging Republicans in the Senate.

The bill's advocates say that they have garnered an overwhelming number of votes in the House and Senate and the support of President Donald Trump — exactly as McConnell has asked. They believe they have the rare opportunity to alter what they see as unjust sentences of thousands of nonviolent prisoners, and pass a small but important corrective to misguided policies implemented in the 1980s and 1990s. They say the time to pass the bill is now.

Opponents of it — including a core of Republican senators — say it would release early from prison thousands of what they see as dangerous felons, and divide the party. They say the Senate should be focused on other issues in the next few weeks, including confirming judges, and passing the massive Farm Bill and a spending bill to avert a government shutdown by December 7.

McConnell has been hearing the debate rage from both sides. In private luncheons at the Capitol, Republican senators have parried points that have spilled out into public. He's heard from at least one advocate from Kentucky, Holly Harris of the Justice Action Network, who says she showed him polling of how prison and sentencing reform is popular in Kentucky. (Opponents of the bill say the poll's methodology is flawed).

But McConnell has said little, except that his team will whip to find "what the consensus is," as the issue continues to bitterly divide Republicans in the Senate. His office declined to further comment to CNN for this story.

Lawmakers eye 'First Step'

The legislation, known as the First Step Act , would allow some current and future prisoners to get out earlier, and rehabilitate into society through halfway houses, home confinement or other supervision, by reducing drug-related mandatory sentences and making more offenders eligible for early release. For a prisoner to reduce his or her sentence, they'd need to be determined by the Bureau of Prisons as a "low risk" for recidivism and earn credits through certain activities and programs.

The United States has the highest incarceration rate in the world. There are well over 2 million adults in American jails. The vast majority are in state and local prisons; There are more than 180,000 federal inmates. The First Step Act addresses that population, and its advocates say the bill is exactly that: a first step toward a broader overhaul of the US criminal justice system.

It's difficult to determine exactly how many prisoners would be affected by the bill. Ames Grawert, a senior counsel at the Brennan Center for Justice, which is in favor of it, pointed CNN to 2018 Congressional Budget Office figures estimating the impact of various sentencing reform provisions in a separate bill that were included in the First Step Act.

The First Step Act would retroactively apply the 2010 Fair Sentencing Act, which reduced the disparity between powder and crack cocaine-related offenses, aiding around 2,600 prisoners, according to that CBO report. More than 2,000 people entering federal prison annually would receive lesser sentences — around 20% shorter — than under current law with the expansion of a "safety valve," which allows judges more discretion in waiving mandatory minimum sentences in certain cases. The new credits could help many federal inmates get out of jail sooner.

"The FIRST STEP Act's 'good time credit fix' will give every prisoner a chance to earn around seven extra days off their sentence per year -- effectively helping a lot of people a little bit," said Grawert. "But by making commonsense reductions to overly-long federal drug sentences, the bill's new sentencing reform provisions will help a few people a lot, and reduce racial disparities in prison in the process."

The bill could change.

Sens. John Cornyn of Texas and Dick Durbin of Illinois, the number-two ranking Republican and Democrat respectively, discussed in the Senate gym Thursday morning potential compromises that could get wary Republicans on board.

"This is a once in a political lifetime opportunity," Durbin said.

In a separate interview, Cornyn said that addressing some of the concerns of one law enforcement group — the National Sheriffs' Association — would "guarantee" the support of some Republicans. Cornyn, the GOP Whip, said his job was to give McConnell "an accurate count of where the votes are," rather than arm-twisting members into voting for it. He also noted that "our time is limited" in getting it done.

Many Democrats are in favor of the bill — Durbin, the Democratic whip, said his party's "support for this measure is solid." If the Senate can pass it, the House is expected to easily do so too.

Opposition to Trump-backed bill from Republicans

This has left the fight to Republican members of the Senate.

Sen. Rand Paul, a Republican from Kentucky, told CNN that there's a generational divide within the party on the issue.

"I think there are people who were teenagers in 1937 watching 'Reefer Madness' and they're still concerned that Reefer Madness is going to take over and everybody is going to become zombies, hacking and killing everyone if they smoke pot," said Paul, a supporter of the bill. "And then there are a couple of generations after 1937 of people who don't see it with the same degree of evil."

"We had one of the senators in the lunch saying, 'You know how you get no recidivism? Don't ever let him out of jail. Zero recidivism!'" added Paul, referring to a closed-door meeting GOP senators held this week.

Paul did note that there were exceptions to his theory, including 85-year-old Judiciary Chairman Chuck Grassley, a sponsor of the bill.

In response, Sen. Tom Cotton of Arkansas, one of the fiercest opponents of the bill, said he didn't think any mandatory minimums should be reduced since "we're in the middle of a drug epidemic."

Of the generational gap, Cotton, who at 41 is the youngest current member of the US Senate , said that "older senators like Rand Paul" — the Kentucky senator is 55 — "take for granted all the gains that we've made because of the tough on crime policies of the 1980s and are willing to abandon those in misguided efforts to have compassionate understanding for depraved felons."

Harris, the criminal justice reform advocate who met with McConnell earlier this week, said, "it is because of this drug problem" that senators should pass the First Step Act.

"The two go hand in hand: individuals who become afflicted with drug addiction obviously become entangled in the justice system," said Harris. "Certainly people in Kentucky and across the country who are impacted by this drug epidemic don't want to throw in the towel on their friends and family members."

She said McConnell was not the obstacle to the bill's passage and "was quite clear that he is not putting his hand on the scale one way or the other" for the bill. Harris claimed that at least 32 Republican senators supported it — over half the 51-member conference.

Trump and Vice President Mike Pence have lobbied the Senate to support the First Step Act. On Monday, Trump held a roundtable discussion in Mississippi boosting the bill, saying "we're looking like we have the votes, as of right now — and maybe an abundance of votes."

Sen. Roy Blunt, Republican of Missouri, said in an interview Friday that at least half of the Republican conference supported the bill.

"If we get to it this year, it'll be largely because of White House pressure," said Blunt, a member of the GOP Senate leadership. "My guess is that at least half of our members are for it and most of the Democrats."