When The Big Sick opens June 23, it will defy box office odds in several notable ways: The $5 million rom-com has a problematic title, it stars a Pakistani stand-up who opened his publicity swing this week by urging college students to “have sex with an immigrant,” and it will platform in only two theaters in pursuit of critical support followed by a slow ’70s-style rollout wedged between a clump of $100 million-plus franchise pictures including Transformers: The Last Knight.

Despite the odds, I think The Big Sick, edgy but warm-hearted, could become a major sleeper this summer, which would make FilmNation happy — it funded production — as well as Amazon, which laid out $12 million for the film at Sundance earlier this year. Its star, Kumail Nanjiani, an original and ingratiating presence, points out that “this movie may normalize how people see Muslims. It may even normalize me.” His performance may persuade filmgoers to overlook the looming behind-the-scenes presence of Judd Apatow, who helped develop the script — but the movie represents Nanjiani’s voice, and is not an Apatow “Trainwreck.”

The Big Sick surfaced in a way that doesn’t happen anymore. The script was written on spec by Nanjiani and his white, Anglo Saxon wife, Emily V. Gordon. Together they set out to tell the story of their own misbegotten romance. Their biggest obstacles are Nanjani’s faithfully Muslim parents, who insist on an arranged marriage — but not to Emily. Yet Emily, in the movie (played by Zoe Kazan), as in real life, develops a near-fatal illness and plunges into a coma. In the end she overcomes both the coma and the parents.

In scripting their personal story, Nanjiani and Gordon had the guidance of Apatow and Barry Mendel, both veterans of the rom-com scene. Upon submitting the script to FilmNation, they were amazed when Glen Basner, who heads the gutsy indie company, read the script and closed the deal within 48 hours, then auctioned the finished picture, directed by Michael Showalter, at Sundance to the ever avaricious Amazon.

It was Apatow who went apoplectic this week, of course, advising Sony Pictures to “shove your clean versions up your ass” in response to a Sony initiative to sell edited versions (i.e., sanitized) of movies directly to consumers. Still, as Apatow movies go, The Big Sick, despite its R-rating, is a relatively clean-cut account of an unorthodox love affair. As in all Apatow movies, the sharp conflicts are followed by lots of warm hugs.

Early test screenings are eliciting strong responses. “I’m even getting good reviews in Pakistan,” says a surprised Nanjiani, who emphasizes in his appearances that the story is true. “There’s a healthy discipline incurred when you pursue a true story,” observes Holly Hunter, who plays Emily’s mother.

For Nanjiani, The Big Sick represents a radical career departure. Born in Pakistan, he emigrated in his teens. Finding himself at Grinnell College in Iowa, he recalls, “I entered a devout Muslim virgin, but graduated as a Rastafarian with an American girlfriend. Being a fish out of water is how you evolve, and I was way out of water.”

Kumail Nanjiani Emily V Gordon
REX/Shutterstock

Nanjiani labored for several years on the stand-up circuit, getting his TV break on HBO’s Silicon Valley where he plays off his cool nerdiness. “When Kumail and his wife first told me their story, I was totally captivated by them as a team,” says Mendel, who has co-produced films from Bridesmaids to Munich. “He captures the realism and she conveys he emotion.” The movie, Mendel concedes, “deserves a better title, but no one could think of any.”

Basner, president of FilmNation, hopes The Big Sick will mark a triumphant 10th year for his low-profile company, whose projects have included The King’s Speech, Arrival, Nebraska and The Imitation Game.

As an indie, FilmNation has consistently delivered annual grosses topping $125 million per year. On The Big Sick, it sold off some foreign territories. Lionsgate and Amazon distribute in the U.S. Amazon controls the marketing, and plans to rely on Nanjiani and wife to work premieres and other events as stand-ups. The couple is even doing their stand-up routine for key exhibitors via phone.

“We want filmgoers to see the universality of this story, not the ethnicity,” according to one Amazon spokesman. “We want Sick to be this year’s Manchester By The Sea.”