Sigourney Weaver as Elaine Barrish. (USA Network/DAVID GIESBRECHT/USA NETWORK)

Washington should feel flattered by the attention it’s been getting from television in the past few months, most of it surprisingly good.

HBO’s movie adaptation of the 2008 McCain-Palin agonistes, “Game Change,” was a fine bit of reportorial theater-in-the-round for election wonks, but the real springtime blossom was the apolitical comedy series “Veep,” also from HBO, starring Julia-Louis Dreyfus as a neurotically egocentric vice president with animosity to spare. To those two we should add the ridiculously guilty pleasures found in ABC’s “Scandal” (from “Grey’s Anatomy” creator Shonda Rhimes), which nimbly turned the dark art of political crisis-management into a soapy form of camp featuring that rarest of broadcast creatures: the strong, black female lead.

Victories all, in one way or another, and it’s worth noting that each hinges on telling its story from a woman’s point of view. Maybe this was the secret all along to making a good “Washington” TV show. Our town’s most interesting characters are the women, not the men.

“You know, I am just sick of it all,” confesses Elaine Barrish Hammond, the Hillary-esque secretary of state and former first lady played with delicious determination by Sigourney Weaver in USA’s fun, fizzy “Political Animals,” a six-part miniseries that begins Sunday night.

“I am sick to death of the [B.S.],” Elaine confides to her chief-of-staff son, Douglas (James Wolk), behind closed doors. “The egos and the men. I am sick of the men. Just one time — just once — I would like to accomplish something in this city without having to spend all my energy navigating the shortsighted, selfish, self-involved and oh-so-fragile male egos that suck up all the oxygen in this town. It makes me so sick, Douglas, so sick I could puke for days.”

So there! “Political Animals” comes from creator Greg Berlanti, whose previous work includes some niche favorites (“Everwood,” “Brothers and Sisters”) and a couple of under-loved attempts, such as “Eli Stone” and the quasi-Kennedyesque past-becomes-future drama “Jack and Bobby.”

Here, Berlanti and his cast waste no time reveling in material that is extra-buttered Washington popcorn. Although the world is not yet clamoring for a strictly biographical Hillary Clinton miniseries (since the story is clearly unfinished), the time is definitely ripe for some fictional workout. At its best, “Political Animals” delves deeply into the unknowable: Why would a first lady remain with her husband after his Lewinsky-like dalliances in the Oval Office lead to permanent shame? Where does ambition overtake emotion — and common sense? What does this resiliency look like when no one else is around? At times, “Political Animals” is as satisfying as Curtis Sittenfeld’s 2008 novel, “American Wife,” which imagined the interior life and thoughts of a Laura Bush analogue.

“Political Animals” is helped enormously by the fact that, after a lifetime spent on the frozen-food aisle, Hillary Clinton herself has become hip of late, partly for her inexhaustible efforts as secretary of state, but also for reasons that will remain forever intangible. After years of not liking her as a wife or politician, America finally warmed to Hillary as a stern diplominatrix in Chanel sunglasses. (For proof, look no further than the “Hillz” texting meme that caught on a while back.)

That’s the character Weaver is playing here — Hillary with a strong dose of Lt. Ellen Ripley from “Aliens”: vulnerable but fierce, and reliably smarter than all the hapless men around her. “Political Animals” avails itself of a broad timeline, from Elaine’s past as a deceived and heartbroken first lady (“Mao gave that to Nixon!” her husband pleads as she prepares to hurl a Ming vase at him) to her present apogee as a global peacekeeper. It opens during the last presidential primary, when candidate Elaine must swallow her pride and concede to a more charismatic challenger (Adrian Pasdar as the president), who eventually appoints her as his secretary of state.

“Political Animals” then indulges in a bit of national wish fulfillment: With her campaign over, Elaine tells her still-philandering husband, former president Bud Hammond (Ciaran Hinds), that she wants a divorce. For anyone who’s paid rapt attention to the Clinton story for the past 20 years, the catharsis is understandably palpable and very you-go-girl. She’s better off without him.

Yet not entirely. She finds Bud useful as (spoiler alert!) an occasional sex partner and as a high-profile diplomat on missions that call for his ex-presidential smoothness, as when she sends him to Iran to rescue three journalists accused of spying. “I ask you to save the lives of three people, and instantly you think you can save the whole world,” she scolds him. (Hinds, an accomplished Irish actor seen in raft of British dramas and everything from a “Harry Potter” movie to HBO’s “Rome,” is a bit of letdown as Bud, seeming to conjure his cream-gravy caricature from old LBJ telephone recordings.)

Nicely threaded through Elaine’s saga is a pesky “Washington Globe” reporter, Susan Berg (played by the fabulous Carla Gugino), who won a Pulitzer covering the Hammond sex scandal in the ’90s and is now back for some fresh sauce in the form of a long Sunday magazine profile. Susan is motivated by the fact that her deeper journalism no longer matters as much as the thinly reported blog items written by a younger rival.

The rest of the ensemble cast helps pull the show along: By ditching the infinitely boring concept of Chelsea Clinton, “Political Animals” gains two narrative-rich Hammond sons — the gold-standard Douglas (I’m for anything that puts James Wolk, the star of Fox’s ill-fated “Lone Star,” back on TV) and the black sheep T.J. (Sebastian Stan), who came out of the closet while the family was still in the White House and then spiraled into a chronic coke habit. There’s also Elaine’s shrewd mother, played by Ellen Burstyn with the occasional catty hiss.

“Political Animals” verges right up to the edge of ludicrous with the right combination of salty-sweet and silly-smart. In just two episodes, it exhibits better writing, stronger acting, cleaner momentum and more confidence than most new shows ever find. If the secretary of state’s dysfunctional family and bizzaro politics become too much to bear, then, happily, it’s over after six episodes.

But I suspect that Hill — I mean, Elaine — will someday run again.

Political Animals

(80 minutes) premieres Sunday at 10 p.m. on USA.