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 Malloyin “1600 Penn.” (NBC)

The network — which on Monday will officially unveil its prime-time plans for next season, kicking off an orgy of new-sked unveiling known as the Broadcast Networks’ Upfront Week — has ordered a comedy called “1600 Penn.” The show, about a dysfunctional first family, is exec-produced by, among others, former Obama speechwriter Jon Lovett.

Before Lovett left Washington (in September) for Dottyville on the Pacific, he wrote many of President Obama’s speeches about financial reform, seeded laugh lines into Rahm Emanuel’s commencement speeches and wrote gags for Obama’s White House Correspondents’ Association Dinner remarks.

An NBC pickup of “1600 Penn” was considered something of a slam-dunk among TV industry intelligentsia (oxymoronic?) given that NBC’s head of programming, Jennifer Salke, was, until summer of ’11, an exec VP at 20th Century Fox TV — which is the studio behind “1600 Penn.

NBC had great ratings success years ago with a certain White House drama called “The West Wing,” whose writers included congressional staffer turned cable-TV host Lawrence O’Donnell and former Clinton White House speechwriter Eli Attie.

ABC had less success with its White House drama “Commander in Chief,” in which Geena Davis landed the POTUS role.

And in July, USA will unveil “Political Animals,” in which Sigourney Weaver does not play Hillary Clinton but, rather, a former first lady to a philandering POTUS, who runs unsuccessfully for POTUS herself and loses, only to get named secretary of state by the new president.

But it’s unclear whether America embraces the idea of laughing at the first family. Years ago, Comedy Central’s “That’s My Bush,” about the President George W. Bush’s clan, died in infancy. So, too, did the defunct UPN network’s “The Secret Diary of Desmond Pfeiffer,” which imagined a black butler as the real brains of the dysfunctional Lincoln White House.

But more recently, HBO debuted to solid numbers the comedy series “Veep,” in which Julia Louis-Dreyfus plays a senator who becomes VPOTUS and learns that the job is nothing as she’d imagined — and hilarity ensues. It was created by Armando Iannucci, the Scottish satirist who penned the Oscar-nominated “In the Loop.” He’s also exec-producing, as is New York mag’s Frank Rich.

Bill Pullman plays the president of the United States in “1600 Penn,” Jenna Elfman is the first lady, and “The Book of Mormon’s” Josh Gad plays the president’s eldest son, who provides most of the “dysfunction.”

NBC has also ordered a new drama series that’s best described as “House is a veterinarian.” You know — loves pets, hates the humans who own them.