We should have trusted David Letterman.

He tried telling us back in 2000 that Jim Gaffigan was a whiner worth indulging by putting the full weight of his production company, Worldwide Pants, behind the young comedian, much as Letterman had done with Ray Romano, a gamble that paid off big with the long-running sitcom “Everybody Loves Raymond.”

Gaffigan’s first swing at the plate, the 2000-01 workplace comedy “Welcome to New York,” was yanked off the schedule after 13 episodes. His follow-up — a thankless role on “The Ellen Show” as a befuddled ex-boyfriend who appeared to be the only man on Earth in the early ’90s who didn’t know Ellen DeGeneres was gay — seemed to suggest that Letterman’s judgment was clouded by the fact that Gaffigan was a fellow Hoosier.

Ah, ye of little faith.

It took more than a decade, but Gaffigan is finally riding high, with seven performances Wednesday through Saturday at the State Theatre, a stand-up streak previously achieved in downtown Minneapolis only by Larry the Cable Guy. The shows come during a hiatus from “The Jim Gaffigan Show,” a new series that has helped change TV Land’s image from the Geriatric Channel to Comedy Central Light. Earlier this year in Philadelphia, Gaffigan opened for Pope Francis in front of 1 million people, a feat that not even comedy kingpin Kevin Hart can match.

Credit Gaffigan’s work ethic and willingness to trade in his beloved Hot Pockets for humble pie, taking secondary roles in sleeper sitcoms (the 2006-10 TBS series “My Boys”) and gut-wrenching dramas on Broadway (“That Championship Season”), all in the name of honing his chops — and paying the bills for the five children he and his wife are raising in Manhattan.

Through it all, Gaffigan has refused to abandon his obscenity-free routine. You’re more likely to hear a swear word at the Vatican than at one of his acts.

That policy seems to be more popular than ever, now that George Carlin’s seven dirty words can be heard on cable any hour of the day.

Consider Pollstar’s list of the highest-grossing comedy concert movies of all time. The top 10 is dominated by such names as Martin Lawrence, Eddie Murphy and Richard Pryor, performers who peppered their acts with once shocking language. The only “clean” member of that list is also the most recent: 2014’s “The Fluffy Movie” starring Gabriel Iglesias, whose idea of an obscene act is not licking your dinner plate clean.

“I think what makes Jim Gaffigan so appealing to our patrons is his brand of family humor — anyone can come see his show,” said Tom Hoch, president and CEO of Hennepin Theatre Trust, which manages the State. “We’ve heard from a lot of people asking if they can bring their teenagers.

“With his new show on TV Land about balancing fatherhood and comedy, he’s gaining even more popularity. His Midwestern likability attracts audiences.”

Gaffigan didn’t change his act; he just waited for the rest of the country to change its attitude.

“Fame is not nearly as important as it would have been 15 years ago,” he told me in 2013. “Back then, I had a completely different set of priorities. I was probably much more consumed with being successful than being creatively fulfilled. There’s a big distinction. I’m not interested anymore in attaining fame just to have fame.

“In the end, I’d rather be a good dad. I mean, it’s fun to have your ego stroked, but if [the failed-fatherhood ballad] ‘Cat’s in the Cradle’ will be echoing in my ears when I’m in my 60s, it’s not worth it.”

When: 7 p.m. Wed., 7 & 9:30 p.m. Thu.-Sat.
Where: Historic State Theatre, 805 Hennepin Av. S., Mpls.
Tickets: $49.75-$59.75. hennepintheatretrust.org, 1-800-982-2787.