As you watch “The Proposal,” it’s tempting to imagine what one of the masters of screwball comedy—somebody like Preston Sturges—might have made of the threadbare premise of a domineering woman executive, threatened with deportation, who forces her assistant to agree to marry her so she can stay in the country. He would have provided lots of clever situations and reams of witty dialogue, of course, and kept things moving at a sparkling pace. He would have had a pair of stars who lit up the screen. And he would have deftly dealt with the inevitable denouement—their falling in love for real.

Alas, that sort of comic fluency seems a dead art, and what we have here is a good example of how things can go wrong. Peter Chiarelli’s script starts decently enough, with a low-rent imitation of “The Devil Wears Prada” as bitchy Margaret Tate (Sandra Bullock), editor-in-chief over a publishing empire, lords it over the office, most notably her doormat assistant Andrew Paxton (Ryan Reynolds), an aspiring writer himself. A scene in which she abruptly fires her second-in-command (the amusing Assif Mandvi) has some energy.

But when the plot kicks in, the picture quickly goes flabby. To prove the genuineness of their purported romance in the face of a hard-nosed INS investigator (Denis O’Hare), the couple jet off to visit his family in Alaska to celebrate the ninetieth birthday of his spunky grandmother (Betty White). While putting on an act for her and Andrew’s parents (Craig T. Nelson and Mary Steenburgen), they find themselves actually drawn to one another—especially after the family convinces them to marry at once and goes about preparing the ceremony. In process, of course, Margaret’s harsh exterior melts and she shows herself for the vulnerable woman she is. A last-minute bump in the wedding plans almost derails the predictable ending, but fear not: love triumphs.

This is the meat of the movie, and it’s hardly top-grade, the screenplay opting more for sitcom silliness than real wit and relying on the most obvious elements—a cute dog and White’s feisty old lady—for laughs. (The actress is still a treasure, but when she’s reduced to dressing up in Indian garb and dancing around a fire to a pre-recorded drum, she’s being badly misused.) Even more unhappily, we’re treated to one of those stereotypical local characters who’s a jack of all trades (sort of a Alaskan version of Pat Buttram’s Mr. Haney)—in this case Ramone (Oscar Nunez), a shopowner, minister and (horrible to say) exotic dancer. Especially in that last incarnation, he’s actually creepier than funny.

Worse, the percentage of comedy swiftly declines as bathos increasingly takes over. Screwball can endure a soupcon of sentiment, but not this much. And director Anne Fletcher, whose only previous effort of note was the fluffy chick flick “27 Dresses,” indulges the mawkishness rather than tamping it down, slowing the action to a crawl. One might have expected so expert a choreographer to keep the movie lighter on its feet.

The stars aren’t very effervescent, either. Bullock manages the hard-as-nails broad business of the early scenes well enough, but as the character softens she slips into her tired old mannerisms. Reynolds, meanwhile, continues to seem a size or two too small for the leading-man roles to which he and the equally insufficient Bradley Cooper are being assigned nowadays. He has a certain boyish charm, but lays it on too thick, as though aware he doesn’t offer much else. Of the others, Steenburgen and Nelson are pretty much wasted, White does what she can with inferior material, and Nunez never recovers from that appalling dance routine (set to Frankie Goes to Hollywood’s “Relax,” of all things). As for O’Hare, he’s stuck with a character as irritating as the debt collector in “Confessions of a Shopaholic,” and makes him equally detestable.

“The Proposal” has an attractive look—the pseudo-Alaskan locations are lovely, and they’re well caught by cinematographer Oliver Stapleton. But Aaron Zigman contributes one of those annoyingly perky scores that italicizes every supposedly mirth-inducing moment.

Sluggish when it should be scintillating and sappy where it should be sardonic, this romantic comedy winds up more softball than screwball.