Perhaps it’s a sign of how times have changed that when Judy Holliday played ditzy Gladys Glover, who in the 1954 comedy “It Should Happen to You” rented a Columbus Square billboard simply to put her name up on it, her character was portrayed as a charming kook who gained an unexpected measure of recognition—and love, of course—from her spunky prank. “Welcome to Me” is also about a woman who seeks fame in an unusual, but more modern, way—by financing her own television talk show from her lottery winnings. But sixty years later charm proves in short supply, and tonally the movie owes less to Holliday’s than to Martin Scorsese’s dark, mordant “The King of Comedy.” Instead of Garson Kanin’s effervescent lark, Eliot Laurence and Shira Piven serve up a penetrating but unsettling portrait of a woman with borderline personality disorder who finds a weird kind of notoriety by indulging her obsession with celebrity culture—and by extension a more general satirical take on the narcissistic impulses so prevalent in today’s society.

As the film opens, Alice Krieg (Kristen Wiig) is a semi-recluse who spends most of her time in a cluttered apartment in a dusty desert town, watching tapes of old “Oprah” programs and self-improvement infomercials. Occasionally she visits her long-suffering court-appointed psychiatrist Daryl (Tim Robbins), who encourages her to get back on her meds. She has only one true friend, Gina (Linda Cardellini), who drops by occasionally to offer support.

One of Alice’s few pleasures is to play the lottery, and she suddenly finds herself an $86 million winner. Moving into a suite in a nearby casino, she celebrates with her parents, Gina, and her gay ex-husband Ted (Alan Tudyk) and his partner. Then she decides to go to the broadcast of a program on a small local TV station, on which huckster Gabe (Wes Bentley) is ineffectually promoting a herbal supplement. From the studio audience she virtually commandeers the program with her odd remarks when invited to the stage, and she abruptly offers Gabe’s brother Rich (James Marsden), who runs the place, $15 million to give her a two-hour talkshow over which she’ll have complete control. To the horror of his staff—including producer Dawn (Joan Cusack) and her assistant Deb (Jennifer Jason Leigh)—cash-hungry Rich promises to fulfill her every whim.

That includes acquiring a swan boat like one from “Parsifal” that she demands for her entrance at the top of the show, as well as a kitchen set where she conducts strange cooking segments and even odder self-help ones in which she discourses with shocking explicitness about her own condition. But Alice’s main focus is on strange, high-pitched recreations of episodes from her own life that traumatized her, in which she excoriates by name those she holds responsible for her torment (like a girl she accuses of having messed with her makeup case at camp). She’ll also come on to the kindly Gabe and to Rainer (Thomas Mann), an admiring graduate student who becomes a fascinated fan after the show incredibly gains a cult following, though her attitude even in their most intimate moments together remains curiously perfunctory.

Matters can’t continue without turmoil for long, of course, and as Alice’s antics escalate—she employs her experience as a veterinary aide to begin neutering dogs live on air—station lawyer Barb (Loretta Devine) is bombarded by lawsuits from those she’s offended. The brouhaha leads to a full-scale nervous breakdown, compounded when Daryl cuts her off as a client and Gina walks out on her because of her selfishness; that ultimately encourages a change of heart while bringing no cure. And so while Alice’s show ends with a bang—a telethon, no less—that doesn’t mean her condition won’t go on.

There are flashes of genuine brilliance in “Welcome to Me,” and Wiig is at her deadpan best as Krieg, conveying the character’s unnerving single-mindedness with near-frightening intensity. And yet the film’s very success in succeeding at what it sets out to do engenders disquiet: it captures the reality of mental illness but then invites us to laugh at it. Wiig doesn’t plead for understanding or sympathy—in her hands Alice never degenerates into a “cute,” lovable oddity, like Dustin Hoffman in “Rainman” for example—but at the same time she’s meant to be a darkly humorous character. And when you do chortle over her insanely over-the-top excesses, you’ll probably be more than a little queasy about doing so. The effect is rather like visiting one of those old carnival sideshows where people from a Tod Browning shocker would be on display for the amusement of a callous crowd. It’s aesthetically admirable that a movie would aim to create a sense of unease in its viewers rather than just satisfy them with conventional nostrums and platitudes. But using mental imbalance as a means of satirizing our contemporary obsession with fame will disturb a lot of viewers, and it leaves “Welcome to Me,” for all its virtues, an ethically debatable proposition.

Moreover, while the film is uncompromising in going that route for the first hour or so, in the last act it holds back, opting for a resolution that, while hardly sunny and comforting, is reluctant to take the approach as far as it might go. So on the one hand its initial take on the subject may cause many viewers to cringe, but on the other once it’s established such a damn-the-torpedoes attitude it loses its nerve in the final stretch.

You have to respect a film that takes the risk of alienating viewers, and to admire the fearlessness of Wiig’s performance. But you also have to accept the fact that in the end the result, while fascinating, is as deeply flawed as its protagonist.