From left, Benjamin Stockham as Xander, Martha MacIsaac as Becca, Bill Pullman as Dale, Amara Miller as Marigold, Josh Gad as Skip, Jenna Elfman as Emily, Andre Holland as Marshall Malloy in “1600 Penn.” (Chris Haston/NBC)

NBC’s White House sitcom “1600 Penn” comes off as a fairly formulaic yet occasionally bright return to an old premise: Wouldn’t it be funny if the first family was just as madcap and dysfunctional as the rest of television’s manufactured broods?

In real life, the White House’s occupants are beloved by many and loathed by some, but, by necessity, they’re a tad stiff. When President Obama and his wife, Michelle, let Barbara Walters or some other observer in, the banter is light and predictably cool — they’ve got the “dorky husband/adept wife” Huxtable shtick down pat.

The Obama daughters, meanwhile, have entered adolescence under the unwritten but fully understood Chelsea Accord, which keeps the news media at a safe distance; what little we know about them comes from their parents, who emphasize discipline, homework, balanced diets and rationed WiFi. As a result of this careful image-tending, we’ve seen Barack Obama have more spontaneous and even comedic fun with other people’s children — such as that recent photo of him goofing around with a young visitor dressed as Spider-Man.

“1600 Penn,” which premieres Thursday night (viewers got a sneak peek at the pilot episode in December), isn’t all that bad as a vicarious and over-the-top riff on what it’s not like to live in the White House. Such parodies include everything from “That’s My Bush!” to “Dave” to a hundred “Saturday Night Live” sketches. This all goes back at least as far as Vaughn Meader’s “First Family,” a Kennedy-esque comedy routine and best-selling record album that came to a swift halt after the 1963 assassination.

Here, there’s no danger of a partisan storyline or any resemblance to the current administration — even if one of the writer/producers, Jon Lovett, is a former Obama speechwriter.

Josh Gad plays Skip, the president’s oldest son. (Jordin Althaus/NBC)

Bill Pullman stars as President Dale Gilchrist, a taciturn commander-in-chief who is not far off in demeanor from the alien-fighting POTUS that Pullman played years ago in “Independence Day.” Jenna Elfman — terrific in her “Dharma & Greg” years and still sorely in need of worthier material — plays the president’s newish, younger wife, Emily.

She’s a first lady who must prove herself not only to her stepchildren but also to a skeptical nation. At a photo-op with schoolchildren, one child asks the first lady if she’s a trophy wife; later she has a showdown with the chief of protocol. “I’m tired of the passive-aggressive history lessons,” Emily snaps. “ ‘Jackie Kennedy did this’ and ‘Dolley Madison did that!’ Guess what — on Dolley’s watch, this place burned to the ground.”

Skip, the eldest of the four Gilchrist children, is a lovably hapless oaf played by Josh Gad. He is summoned home to the White House after one too many mishaps in his seventh lackluster year of college. The show immediately invests too much of its energy on Gad’s narrow performance, in which he delivers nearly all his laugh lines in a Jim Gaffigan-style stage whisper. Skip’s doofus demeanor is funny for about two scenes in the pilot, but it begins to shred apart by the third episode. This may be an irreparable situation, since Gad is also an executive producer.

Even as Gad’s character hogs screen time, the rest of “1600 Penn” improves when the show gains a little traction. As the Gilchrist family’s neurotic overachiever, Becca, Martha MacIsaac is more in line with a character one might find roaming the halls between the East and West wings. “1600 Penn’s” major arc so far centers on Becca’s unwelcome discovery that she’s preggers — the result of a rare night of reckless abandon with a handsome young stranger she meets in a bar.

Becca confesses this to her stepmother, unfortunately while both women are wearing live microphones during a break in a TV interview. A full-on Washington scandal erupts as White House reporters pelt the press secretary (Andre Holland) with questions about the baby-daddy: “Is it the physical therapist from Bethesda?” asks one. “Is it the puppeteer from Wichita Falls?” asks another. (“Reporters are the worst people in the world” is the Gilchrist family mantra.)

A livid President Gilchrist summons his intelligence command and quickly locates the young man in question, D.B. (Robbie Amell), working at an Old Navy in a mall in Friendship Heights. (Um, is there an Old Navy in a mall in Friendship Heights? This reminds me of the time “The West Wing’s” C.J. Cregg ran off to some mythical downtown Barney’s — not the Barney’s Co-Op, mind you — to fetch a last-minute frock. Hollywood has no clue how underserved Washington’s retail addicts really are.)

Secret Service agents are dispatched to haul the unwitting D.B. in for a presidential grilling. Only then does “1600 Penn” start to show signs of a “Modern Family”-like spark, as Amell’s version of a well-meaning half-wit both complements and outshines Gad’s Skip. “Can you take me back to the mall?” D.B. asks. “Not the Lincoln Memorial-y one, the real one.” Watching him, you’ll rightly wonder if maybe there could be a decent sitcom here after all, so long as the writers continue pushing toward absurdity.

In another time — perhaps those fallow years after “The West Wing” — “1600 Penn” would have been a pleasant respite, if only because so many Beltway-centric shows turn out to be duds. But we’re in a kind of golden zone right now, with serious fare (Showtime’s “Homeland”) mixed in with the laughably melodramatic (ABC’s “Scandal”) and the earnestly soapy (USA’s miniseries “Political Animals”). It finally feels like Washington — or someone’s warped notion of it — belongs on scripted television.

As for comedy, it would be difficult to outdo HBO’s wickedly hilarious “Veep,” which makes “1600 Penn” look like a half-finished improv sketch. But give a few points to “1600 Penn” for trying.

1600 Penn

(30 minutes) airs Thursday at 9:30 p.m. on NBC.