One of the great things about Billy Bob Thornton is that he’s such an ornery crust-bucket. Directors can toss him into the most potentially saccharine fare, and he’ll squeeze out just enough vitriol to trick you into thinking it’s all really a sarcastic mockery of Hollywood sentimentality.

And then it’s too late. You got suckered, and now your tear ducts are leaking like lawn sprinklers and you hate yourself for being so gullible. Whether as “Bad Santa” or the burliest of “Bad News Bears,” the wired and wiry actor often is less redneck sociopath than secret love panda.

That dual nature makes him ideal as the fallen star-man of “The Astronaut Farmer.” The film, written by the twin-brother team of Michael and Mark Polish (“Twin Falls Idaho,” “Northfork”) and directed by the former, follows that unfortunate convention of coy yet painfully unclever joke titles: Mr. Thornton is a former astronaut named Charles Farmer who gave up outer space to save his family’s farm.

The squelching of his dream is a shame, but he’s doing all right. His wife (Virginia Madsen) is sexy and sassy. His two little girls (played by young members of the Polish brood) are beyond adorable. His teenage son (Max Thieriot) worships him and aspires to be an aerospace engineer, just like dad. And Farmer’s father-in-law turns out to be a kindly old Bruce Dern (one of the 1970s signal Hollywood astronauts in “Silent Running”), whose character is named “Hal,” another Polish in-joke, in honor of the nutty supercomputer from Stanley Kubrick’s “2001: A Space Odyssey.” (One of the Farmer munchkins also is named “Stanley,” another large clue to the filmmakers’ sensibility.)

In fact, though, Farmer is in sad shape. The bank is about to repossess and auction off his Texas farm, and everyone thinks he’s a wacko. Why? Because he’s building a rocket ship in his barn that he intends to fly into outer space, that’s why. That audacious premise, coupled with the long odds this stubborn coot takes on, gives the movie a strangely compelling focus. Whether the Polishes intend this mission impossible to be some kind of metaphor for an endless war in Iraq, or merely wanted to turn Mr. Thornton loose amid Coen Brothers-lite red state wackiness, is hard to determine.

What’s easy to sort out is the sense of all-American wish fulfillment, served up at a time when much of Middle America must be feeling about as emotionally burnt out as Mr. Thornton nearly always looks. The story prolongs the inevitable decisive moment as much as it can, as Farmer is stalled by Homeland Security, NASA, and the Federal Aviation Administration, chastised by an old astronaut buddy (Bruce Willis, in another of his stellar walk-ons), and besieged by a press that he skillfully manipulates before it turns savage on him. He endures dark nights of the soul and a domestic meltdown that hastens a do-or-die decision and … well, let’s not give the game away.

The improbability of it all, oddly, is what’s most improbable about the premise. Private corporate space programs that bid to profitably launch Bill Gates-types into brief and expensive visits to near space are already a reality. And the weirder aspect of Farmer’s plight is that, logically, someone with a NASA résumé who can build his own rocket should be able to get a high-paid gig at some level of the military-industrial complex — especially with a war on.

Even for a comedy with dramatic drive, “The Astronaut Farmer” demands that the audience suspend its disbelief on multiple fronts. Although, perhaps, this is all less amazing than the recent headlines about a real-life astronaut on an alleged homicide mission, driving hundreds of miles in a diaper to wreak vengeance on a romantic rival. But as Sister Rosetta Tharpe once sang, “Strange things are happening every day.”

What is believable, however, is the passion of the Billy Bob. He genuinely makes all the tearjerker, hug-a-munchkin family stuff resonate. Maybe it takes an actress as sensual and earthy as Ms. Madsen to match Mr. Thornton in emotional honesty, but their grown-up dynamic is what keeps the movie from drifting out of orbit.

Cornball as it is, when she tells her space-suited hubby she wants him back in time for dinner, you really want him back there, too.