Sen. Mike Lee (R-Utah) is a main backer of the First Step Act, a bill to reduce mandatory minimum sentences for nonviolent offenders in federal prisons and to allow some people to be incarcerated closer to their homes. (Jim Lo Scalzo/EPA-EFE/Shutterstock)

Movies and Capitol Hill tend to mix mostly in throwback work like “Mr. Smith Goes to Washington,” or in token scenes in popcorn fests such as “Mission: Impossible,” in which lawmakers try to rein in renegade heroes. Otherwise? Policy and protagonists tend to stay pretty far apart.

But a prison reform bill in the Senate improbably owes at least some of its momentum to a movie — not a widely seen Hollywood release but a little-known documentary that has quietly been marshaled by the bill’s backers to sway skeptical lawmakers.

As the much-covered First Step Act stands on the brink of passage, the film, an emotional look at a family caught up in the federal prison system titled “The Sentence,” appears to have assisted in getting it there.

“This movie has really helped to get people to understand. It’s a key part of the groundswell of support behind this bill,” Sen. Mike Lee (R-Utah), a main supporter of the First Step Act, said in an interview with The Washington Post.

The First Step Act aims to, among other goals, reduce mandatory minimum sentences for nonviolent offenders in federal prisons and to allow some people to be incarcerated closer to their homes, which would reduce the burden on their families. While many reform activists say the bill calls for a modest action that will affect only a small number of inmates, they also note its importance in making the punishment for nonviolent offenders more proportional.

The bill still has some opponents, including Sen. Tom Cotton (R-Ark.), who argues it will put violent offenders on the street. But with backing from President Trump and a wide swath of Republicans and Democrats (Newt Gingrich wrote an op-ed in The Post), passage seems likely. Sen. Lindsey O. Graham (R-S.C.) has said as many as 80 senators could wind up voting for it. The House has already passed a version of the bill.

After previously delaying a vote, Senate Majority Leader Mitch McConnell (R-Ky.) this week said he will bring it to the Senate floor by the end of the month, offering a high-profile coda to a years-long battle.

[Update, 5:49 p.m. Thursday: After the Senate passed the bill on Wednesday, 87 to 12, with nearly 30 Republicans joining the entire Democratic caucus, the House on Thursday passed that version of the bill, 358 to 36. It now moves to President Trump to sign.]

“The Sentence” has been taking a more humble path.

The movie is directed by first-time New York director Rudy Valdez, who picked up a camera a decade ago when his sister Cindy Shank, a Michigan mother of three, was sentenced to 15 years in prison under mandatory minimum laws. Shank many years before had lived with a boyfriend who was a drug dealer. While prosecutors said she did not participate in selling drugs, she was still guilty under drug conspiracy laws that criminalized sharing a home with a dealer.

Shank would go on to serve nine years in a federal prison before being among a rare few granted clemency at the end of 2016. During her time behind bars, her three daughters grew up with Shank’s husband. The girls' relationship with their mother was limited to tightly timed weekly calls; one child took to calling the phone “Mommy.” Valdez was there capturing all of it, often shooting the children, unguarded, living in the cruel reality of their mother’s incarceration.

The film was so brutally effective that, at its Sundance Film Festival premiere in Park City, Utah, in January, strangers alternately came up to hug the girls and vowed to Shank and Valdez that they would join the campaign for criminal justice reform. (The family’s experience at the festival was chronicled by The Post.)

But after Sundance, the movie debuted to minimal fanfare on HBO in October, taking a back seat to documentary smashes “RBG,” “Three Identical Strangers” and “Won’t You Be My Neighbor.” Like “The Sentence,” those three movies also premiered at January’s Sundance, but, in contrast, went on to gross a combined total of $50 million in theaters.

Yet the right people were taking notice. Lee’s staffers became aware of “The Sentence” after the Sundance premiere happened in their backyard and alerted the senator who, since his election in 2010, has been a crusader for criminal justice reform.

Lee said he saw it and thought this could be a tool to convince politicians, particularly Republicans, who were skeptical that sentencing laws needed to become more flexible. He hosted a screening at a Senate office building with Sen. Cory Booker (D-N.J.) and showed clips at a weekly steering lunch he holds with fellow Republican lawmakers. He also went on such shows as MSNBC’s “Morning Joe” with Valdez to extol the movie.

Soon, staffers and fellow lawmakers were stopping to tell him they had seen it and were thinking about mandatory minimums differently. “People became emotionally engaged watching it,” Lee said. “A story like this humanizes the issue and changes minds in a way nothing else can.”

That moment crested, perhaps, when Kelley Paul, the wife of Sen. Rand Paul (R-Ky.), who has pushed hard for Congress to pass the First Step Act, urged on Twitter last month for Cotton to watch the film.

"@SenTomCotton watch @TheSentenceDoc @HBODocs to understand the pain and injustice of mandatory minimums on nonviolent people & their kids,” she wrote.

Meanwhile, Valdez and Shank worked their own channels. The day after the Lee-Booker screening, they made the rounds on Capitol Hill to visit lawmakers. “We were walking in these congressional buildings, and all these people were stopping us to say they’d seen the movie and wanted to learn more about Cindy,” Valdez said. “It felt like we had reached people in a different way than they were used to."

Those efforts came on top of the film’s social impact campaign, backed by HBO and producer Park Pictures, that enlisted groups as wide-ranging as the ACLU and the issue-specific Families Against Mandatory Minimums (FAMM). The bill has drawn the support of groups across the ideological spectrum, with many on the left but also a large number on the right, including FreedomWorks and the Koch Brothers' Right on Crime. (The movie, it should be noted, also comes as part of a wave of documentaries on the topic over the past several years, including Ava DuVernay’s “13th.”)

There’s still a chance the First Step Act could stall on the Senate floor. It’s impossible to know how much the documentary changed lawmakers' minds. Trump’s support for the law — an earlier version of which was also backed by former president Barack Obama — has given Republicans cover, as has support from libertarian groups aligned with billionaire industrialist GOP donors Charles and David Koch.

Still, “The Sentence” at least seems to be prompting lawmakers to think in less partisan terms.

That’s in part, Valdez says, because it doesn’t traffic in politics. The director said he made it that way deliberately, “as a human film,” with very few pundits or much larger political context, because that’s how his family was experiencing the problem: as people, not policy. “In hindsight, it made sense, but at the time, it seemed risky — it was just a little story of a family,” he said.

Kevin Ring, who runs FAMM, says that, though it was not made with that in mind, a documentary can become a potent lobbying tool.

“We saw this movie and realized it does more in two hours than we could do in 27 years,” Ring said. “It’s one thing to describe the problem. It’s another to see it.”

Lee has his own spin on the idea. “These can be highly technical areas of the law. As a lawyer, I know how easy it is to get buried in code citations.

“A story,” he added, “is a lot more effective than code citations.”