The way Alice Neel rides the edge of something primitive in her work, the physicalness of her process, her alternately agitated and mangy surfaces, her breathtaking brushstrokes, and the hypersensitive obsessiveness of her portraits suggest Neel ranks among the greatest American painters of the 20th century and merits more than a floor of the Whitney.

This celebratory retrospective, ably organized and well installed by guest curator Ann Temkin, is sparkling even if it’s not extensive enough. Maybe it’s a space problem, but we pass too quickly over the early work, then are allowed to slip into a monotonous groove of portrait after portrait that a room of Neel’s shocking depictions of pregnant women would have circumvented. Still, this is a great opportunity to get acquainted with a marvelously gnarly artist.

Neel’s rise and fall and rise isn’t a classic story; the highs aren’t as high as the lows are low. Born in 1900 to a middle-class Philadelphia family, Neel studied art, married Cuban painter Carlos Enríquez, and moved to New York in 1927 with him and their infant daughter, Santillana. You can see them in what might be the last purely innocent image she would execute for 35 years, a 1927 watercolor in which a topless Neel sweetly diapers the baby, who sprawls in Carlos’s lap.

Then the bottom fell out: Santillana died of diphtheria. Neel gave birth to another daughter, Isabetta, 11 months later, but the child was immediately taken away to Cuba by Carlos. Finally, in 1930, Neel had a breakdown and attempted suicide; she was institutionalized on and off throughout 1931. “I died every day,” she said. But, in a quality that would serve her well, Neel willed herself to paint, took four lovers in seven years (including a sailor, Kenneth Doolittle, who burned hundreds of Neel’s works in 1934), and gave birth to two more children by different fathers.

Neel is an up-and-down artist, but her beginning is almost all up. At the press preview, a critic cracked, “She’s like Soutine lite.” Not true. Soutine was an expressionist head to toe; Neel adulterates her expressionism with heavy doses of reality, visionary flights of fancy, and something bordering on the schizy. In a way, her work is the opposite of Alex Katz’s—his art is angular, cool, lean, and lanky; Neel’s is saggy, roiled, weird, and rumpled. The nine early paintings and six watercolors here, done in a naive expressionist-meets-Social Realist style—especially those of Carlos, her children, lovers, and a swarthy friend named Nadya—are among the most convincing of her career. One or two of these rate among the century’s most intimate, strange, and clever pictures of sex in the city.

One, an untitled watercolor from 1935, is a heartfelt scene familiar to lovers of all persuasions. We see Neel and her sweetie, John Rothschild, in a postcoital bathroom scene. Neel sits on the toilet, her rosy vagina visible, her eyes spaced out, cheeks aglow. Rothschild holds his still erect and reddened penis over the sink to pee. It’s a private Kama Sutra moment.

But in Joe Gould (1933) Neel outdoes herself. Gould (1889-1957), Village person par excellence, sits naked and spread-eagled, like a satyr on a stool. Staring at us with demonic eyes, his balding brow framed in tuffets of hornlike hair, he sports three penises. These aren’t idealized dicks or the teeny genitals of the gods; these are vivacious pricks, painted by someone who looked at cocks and was pleased and amused by them.

Although she had a hard go of it, Neel’s paintings of this period are often great and predict great things. Then something goes wrong. Saying, “The abstractionists pushed all the other pushcarts off the street,” Neel sits out abstract expressionism. She assimilates some of their space, staining techniques, and brushiness, but by 1941 an overworked, rote muddiness sets in and doesn’t go away until the early ’60s. She’s either painting people and not fleshing out character or painting characters without pushing the paint. This effect could have been offset here by including some of her mysterious landscapes and cityscapes. People might say, “Give her a break. She was a single mother raising two boys in a tiny apartment in Spanish Harlem.” But even if she put her life back on track, she sidelined her art. Still, there are strong works from the period: the haunting, Mexican muralist-style picture of her father in his coffin; the undulating surface in Georgie Arce; and—for a taste of things to come—the sketchy, blotchy blouse in the Matisse-like Young Woman.

Then something gives. In 1960, at the behest or at least nudging of her therapist, Neel, who was pretty much out of it, screwed up her courage and asked poet-critic-curator Frank O’Hara to sit for what turned out to be one very tortured portrait, followed by another, looser one that began her next great period. From this gutsy moment—born, I think, of desperation, ambition, and the knowledge that she had stayed too long outside the art world—Neel reinvents herself and retrieves some of the rawness that had been lost. Over the next 24 years, in these loosey-goosey portraits, she paints a plethora of art-world movers and shakers, strangers, and misfits. While Uptowners were making their way downtown to have their portraits painted by Warhol, Downtowners were going up to 107th Street to sit for this bohemian, auntie-like artist.

Some of the results are amazing. Especially the one of Warhol as a wounded, introverted angel, in which Neel meticulously renders his scars like some modern Saint Thomas. We’re also treated to some scary fashion moments. The artist Louise Lieber wears a blue minidress and a purple macramé hat; art critic Gregory Battcock dons yellow bikini briefs and red socks while, next to him, fellow critic David Bourdon sports a pair of Beatle boots. Henry Geldzahler, curator at the Metropolitan Museum, looks indifferent, if skeptical. During their sitting, Neel—who always used these sessions to gossip and further her career—asked to be included in a show Geldzahler was curating, to which he frostily replied, “Oh, so you want to be a professional?”

Other times Neel had genuine insight: In a picture of art historian Linda Nochlin and her daughter, you sense mixed emotions about motherhood on both sides of the canvas. Also, Neel was never beyond flattery. According to the critic John Perreault, who posed nude, she made his penis larger than it is; she gave the eminent art dealer Ellie Poindexter bosoms the size of basketballs, and knocked a few years off art historian Meyer Schapiro. And pride? She called her picture of Annie Sprinkle—a Larry Rivers-like doozy of Sprinkle wearing little but a garter belt and labia ring—”my New York Olympia.”

By the time she died in 1984, Neel—who saw herself passed over by many of her own sitters (including Geldzahler)—was celebrated as a symbol of what expanding the canon could do. She even wound up on the Johnny Carson show, twice. Who she is to us today, as a painter, is more important than who she was as an icon. This exhibition does much in the way of furthering Neel the artist. Most of all, it does what good shows do: leaves us wanting more.