CBS wanted a smart show about Capitol Hill, so the network brass turned to producers Robert and Michelle King, who had tackled state politics with “The Good Wife.”

“It was right around the budget crisis, the government shutdown. There was an element of insanity out there,” says Robert, 56, perched in their office in Brooklyn’s Greenpoint neighborhood. “Our solution to truly addressing a ludicrous situation in D.C. was with some ludicrous plotting.”

Naturally, the married couple thought of “Invasion of the Body Snatchers.”

Politicians, the thinking went, often behaved like aliens, as if their bodies had been invaded by some outside force and they were not responsible for their actions, which often defied precedent or logic.

“The worry was always, how do you keep this from being earnest? Going to sci-fi seemed like it would certainly inoculate us against that,” says Michelle, 54.

Earnest is the last thing you would label “BrainDead,” the 13-episode series that debuts tonight at 10 p.m. It features a meteor, green health juice, a three-decade-old hit by the Cars and, most important, brain-eating bugs.

Mind you, this was all considered before the current election took a decided left turn (or right, or both) to uncharted alien territory. The presidential race is a backdrop, though the season’s last episode will air in August.

Despite the title, the series is not a documentary about the capital’s political quagmire, but a stew of genres. Robert describes it as “the comedy of ‘Men in Black’ mixed with the satire of ‘Network’ and the relationships of ‘The West Wing.’”

The bugs come to Earth via a meteor that lands in Russia, and they travel to America via container ship. In Washington they become devious, powerful and rampant, entering congressmen and their constituents through the ear, eating half the brain and leaving the host ultimately changed. Slime is involved.

The Kings are loath to reveal all but, at least by the end of the first episode, the bugs are not paid for by lobbyists.

Essentially, it seems, they’re a metaphor for Washington’s dysfunction.

“The infected actually get smarter and clearer, more focused and more articulate,” says Tony Shalhoub, who plays Sen. Red Wheatus, R-Md., a Baltimore good ol’ boy, his brain among the bugs’ first brunches.

As a result, they become automaton-like in pursuit of their agendas. As series star Mary Elizabeth Winstead explains, “Nothing gets done. It’s such an absurd explanation for what is really happening in Washington.”

Winstead plays idealistic documentary filmmaker Laurel Healy, who works for her brother, Sen. Luke Healy, D-Md., a politician with a pronounced zipper problem (played by Danny Pino). Laurel says thing like “I hate politics” and “I hate D.C.,” although she hails from a political dynasty “akin to the Gores,” says Winstead, who is shuttling between this show and Richmond, Virginia, for her role as a Civil War nurse in PBS’ “Mercy Street.”

Robert, who penned the 1988 Roger Corman killer-cockroach thriller “The Nest,” explains: “The bugs exploit what is human about the person but makes them even more extreme.” Michelle adds, “The bugs are looking to keep their host in tip-top shape and, as a result, the infected get healthier. They don’t drink. They’re not so interested in sex.”

Instead, the infected imbibe vast quantities of green juice. They constantly play the Cars’ 1984 ditty “You Might Think,” inspired by Robert’s experience of having a former upstairs landlord play Dire Straits’ “Walk of Life” ad nauseam. (The rights to that song proved too expensive.)

The infected also babble in zombielike fashion, although — note to zombie loathers everywhere, and we are a large, overlooked and powerful multitude — this is not a zombie show. The Kings make it clear that half the brain is still operating. The first episode has a fair amount of muck, but no blood.

Despite going buggy, the show is trying to get the politics right. David McCallum, the deputy chief of staff to Senate Minority Leader Harry M. Reid, D-Nev., serves as the show’s Washington consultant. He was recommended to the Kings by D.C. crisis manager Judy Smith, the inspiration for “Scandal.”

McCallum informed the Kings that Laurel would never be hired to do constituent casework on her brother’s senatorial staff, because of nepotism laws.

Robert responded, “Here’s the problem: That’s the basis of the show.”

The writers inserted a line about Luke appealing to the ethics committee for an exception. The line was cut later due to time constraints. Let’s face it: Ethics chatter is stultifying in the face of cerebellum-devouring insects.

Where might senators of opposing parties meet — like that’s going to happen — if one is trying to get the other to switch his vote?

“I suggested the Senate gift shop,” McCallum says. “It’s small, in the basement in the Dirksen building, and nobody hangs around there.”

As for his advice and wisdom, McCallum says, the Kings and the show’s six writers “may listen to you, or they may not.”

Which is so Washington. And Hollywood, too.

“BrainDead’s” soundstage, located a few blocks down (fittingly) Kingsland Avenue from the couple’s office, re-creates sections of the Russell Senate Office Building, including basement quarters for a minority party senator (not true). The wardrobe room has a vast collection of nondescript shirts for men and black pencil skirts for women (true and true). And cherry blossom trees in full flower appear outside virtually every window (if only).

The Kings insist “BrianDead” will be fair and balanced, skewering both Democrats and Republicans.

Christine Baranski, who played Diane Lockhart on “The Good Wife,” says that, on that series, “They tried to see both sides of the story and not write just from the liberal point of view,” often the default Hollywood position. Robert has found comedy in the political divide before, in his screenplay for 1994’s rom-com “Speechless,” about speechwriters working for opposing candidates.

The Kings have mapped out “BrainDead’s” next three seasons — if the series is renewed. The same characters will move to Wall Street.

Michelle notes, “They have a reason.”

Robert, laughing, says, “Wait? Is it that strange that characters would move from Washington to Wall Street? The hard one is the third season, which is supposed to move to Silicon Valley.” The final season would be set in Hollywood.

The theme, Robert insists, will remain the same: “It is all about how our institutions are made stupid.”

With or without the help of brain-eating bugs.