The problem with “The Bronze” isn’t that Melissa Rauch’s Hope Ann Gregory is such a nasty, foul-mouthed, terrible little human being.

It’s that she’s not as funny as the film thinks she is. It’s as if “Bad Santa” and “Bad Teacher” had a kid — and she inherited all the meanness but only a slice of the humor.

This is one of those comedies that could have been a brilliant short film on “Funny or Die” or “Saturday Night Live,” but wears out its welcome as a feature-length film.

Rauch, best known for “The Big Bang Theory” (a show that apparently will never go off the air), co-wrote the screenplay for “The Bronze” with her husband Winston Rauch and plays Hope Ann Greggory, who at the 2004 Summer Olympics suffered a terrible ankle injury — but bravely stuck it out and won the bronze medal, thus becoming America’s Hope. (Shades of Kerri Strug, the similarly high-voiced real-life gymnast who injured her ankle at the 1996 Games but gamely performed one last vault, sealing gold for the Americans and becoming an instant phenomenon.)

Cut to present-day Amherst, Ohio. Hope still lives at home with her sad-sack widower postman father Stan (Gary Cole). Her bedroom is filled with trophies and other memorabilia from her glory days. She pleasures herself to the video of her triumphant moment at the Olympics, she steals cash from birthday cards in her father’s mail truck, she wears her red-white-and-blue tracksuit everywhere she goes, and she spends her days milking the last drops of her local celebrity —getting free sandwiches, abusing the locals, hooking up with random guys and insulting anyone who doesn’t immediately recognize her as the worldwide celebrity she believes herself to be.

Basically she’s delusional AND horrible. What a treat!

When Hope’s former coach dies, she leaves her entire $500,000 fortune to Hope, with the stipulation Hope must coach Maggie (Haley Lu Richardson), a 16-year-old local prodigy and Olympic hopeful. Kicking and screaming and swearing — always, always swearing — Hope reluctantly accepts the assignment.

Maggie is a perpetually upbeat innocent who worships Hope. (Cecily Strong, who plays Maggie’s single mom, is all of 11 years older than the actress playing her daughter.) She’s sweet but she’s kind of an idiot, and she has no idea Hope isn’t really interested in mentoring her.

Hope sets out to sabotage Maggie in the hopes Maggie will quit and Hope can cash the big paycheck. She tries to fatten up Maggie, she sets Maggie up with a guy so Maggie will lose focus, and she schemes and schemes to derail Maggie’s dreams. In the meantime, Hope berates her poor father day in and day out, in scenes more cringe-inducing than witty.

Thomas Middleditch tries hard but is profoundly unfunny as Ben, the gym owner Hope refers to as “Twitchy,” because, well, he has a twitch. Sebastian Stan doesn’t fare much better as Lance Tucker, an impossibly smug and awful Olympics gold medal winner who had an affair with Hope back in the day.

At times “The Bronze” shows flashes of inspiration, e.g., a wild hotel-room encounter between two medal-winning gymnasts. Mostly, though, we’re asked to invest in a movie about a dimwitted, thoroughly unlikable, egocentric, lying brat who isn’t much more endearing at the end of the journey than she was at the outset.

★★

Sony Pictures Classics presents a film directed by Bryan Buckley and written by Melissa Rauch and Winston Rauch. Running time: 100 minutes. Rated R (for strong sexual content, graphic nudity, language throughout and some drug use). Opens Friday at local theaters.