What would you get if you cross-bred Roseanne and The West Wing? Well, yeah, locked up, for a long time. But besides that? The answer might be 1600 Penn. Whether it’s a good answer remains to be seen.

Written and produced by Jason Winer ( Modern Family), Josh Gad ( The Daily Show), Mike Royce ( Everybody Loves Raymond) and former Obama speechwriter Jon Lovett, this attempt to set a slobby dysfunctional-family sitcom inside the White House has its stunningly funny moments. But as the show moves along, there’s a growing suspicion that there aren’t enough of them to sustain an entire series.

Airing as a sneak preview Monday night (the show won’t formally debut until January), 1600 Penn focuses on the neurotic misadventures of a blended First Family headed by Bill Pullman, as a slightly dimmer-bulb version of the gruff chief executive he played in Independence Day nearly two decades ago.

His kids are all in various degrees of trouble, ranging from accidentally burning down a rival fraternity house (“Seven years of college is plenty,” Pullman consoles the suspended boy) to flunking a home pregnancy test (blog headline: WHO DID THE FIRST DAUGHTER DO AND WHEN DID SHE DO HIM?

The kids’ stepmother (Jenna Elfman) is too leggy and blond to have much influence on them or, for that matter, anybody else. When she invites questions from a visiting group of schoolchildren, the first one is: “What does it mean when my dad says you’re a trophy wife?”

All the characters are sharply drawn for maximum comic effect, particularly that of college dropout son Skip. Played by Gad as an amiable but epic screwup, the porcine (favorite snack: jelly-bean-and-whipped-cream casserole) and boobgeois Skip (first thought on visiting the Oval Office: “So much history here. Roosevelt, Superman…”) is a kind of living embodiment of the advice delivered to another collegiate lunkhead a generation ago in Animal House: “Fat, drunk and stupid is no way to go through life, Son.”

But as funny as 1600 Penn can be, after a while the laughs grow fewer and further between. And the misfires are more frequent and painful. Give the show credit for rejecting political correctness, but there are moments when you’ve got to wonder what the writers were thinking. One scene, in which a room full of Latin American presidents get wasted on tequila with the fratboy Skip while they’re supposed to be considering a trade treaty, lacks only a sleeping Mexican wrapped in a poncho and a screechy waiter in blackface to be a dead solid lock for this year’s Stepin Fetchit Memorial Emmy for Egregious Ethnicism.