There aren’t many secretaries of state who make it in show business. Daniel Webster doesn’t count because “The Devil and Daniel Webster” was based on his career as a lawyer and orator, not as a diplomat. Henry Kissinger was a character in the opera “Nixon in China.” The real Condoleezza Rice made a cameo as an ex-girlfriend of Alec Baldwin’s character on “30 Rock.” And that’s pretty much it, unless you count Cordell Hull’s star turn as a member of Franklin D. Roosevelt’s singing cabinet in “Annie.”


So, her other accomplishments aside, Secretary of State Hillary Rodham Clinton is also a pioneer in the world of entertainment. It may be too soon to assess her place in history, but it is already clear that Mrs. Clinton has a huge hold on the public imagination: a woman so well known, and yet so unknowable, that writers and filmmakers keep turning to fiction to try to solve her mystery.


“Primary Colors” was a best-selling novel — and later a movie — about her marriage to Bill Clinton. Mrs. Clinton, as portrayed by Hope Davis, was the real star of “The Special Relationship,” a Peter Morgan docudrama on HBO about the Clintons and Tony Blair. Now Mrs. Clinton’s presidential ambitions — and cabinet post — are fodder for a USA Network television series, “Political Animals,” that begins on Sunday.


Sigourney Weaver plays Elaine Barrish Hammond, a pantsuited former first lady who ran for president and becomes secretary of state. This half-comic, half-serious soap opera à clef could be awful, but instead it is surprisingly fun: a fictional look at Mrs. Clinton that blends what-if alternative history with wish-fulfillment fantasy: if only she would.


Many of Mrs. Clinton’s supporters couldn’t understand why she didn’t divorce her Monica Lewinsky-tainted husband after they left the White House. In this make-believe iteration, the betrayed wife doesn’t stand by her man; she kicks him out. Moments after her concession speech, she leaves the hotel suite, pausing at the door to say to her husband, “Oh, and Bud, I want a divorce.”


Even some of her enemies hated the way Mrs. Clinton was treated by the press. Here, when reporters pry into Elaine’s private life, the secretary of state lets them have it.


“I’m curious, what is it like launching your career by stepping on the throat of someone else’s marriage?” Elaine asks Susan Berg (Carla Gugino), a journalist who won a Pulitzer Prize for writing about Mr. Hammond’s infidelities.


Ms. Weaver is subtle and believable as she channels Mrs. Clinton’s improbable biography and even some of her real-life dialogue. After losing the Democratic nomination to a younger, more charismatic candidate, Paul Garcetti (Adrian Pasdar), Elaine gives a never-say-die speech to her supporters, then accepts a cabinet post, echoing the explanation Mrs. Clinton gave at the time, “When the president asks you to serve, you serve.”


Elaine faces many daunting diplomatic challenges in the job, but one of the biggest is her ex-husband, Bud Hammond, who, since the divorce, has taken up with a bosomy television star half his age.


Unfortunately, Ciaran Hinds plays this make-believe version of former President Bill Clinton so broadly, and with such a cartoonish southern accent, that Bud barely seems qualified to be sheriff of Mayberry, let alone commander in chief.


It doesn’t help that the writers strain for Aaron Sorkinish wit and sometimes badly overreach. “I’m the most popular Democrat since Kennedy had his brains spattered across the Dallas concrete,” Bud tells Elaine. “Baby, I’m the meat in the Big Mac.”


Elaine’s other headache is Susan, who was banished from the Hammond White House for her caustic columns and is still obsessed with finding out the true story behind Elaine’s facade of dignity and public service.


Elaine deserves a more compelling opposite number. Ms. Gugino is pretty and appealing, but her character’s a bit underwhelming as the secretary of state’s Public Frenemy No. 1.


Susan is scornful of the ethics of a sexy younger colleague, saying that if Eve Harrington were around today, “she would bake cupcakes and write a blog.” But Susan’s own code of honor is pretty threadbare: She digs up dirt on one of the Hammonds’ children to blackmail Elaine into granting her an exclusive interview.


Elaine doesn’t have a daughter like Chelsea Clinton, she has twin sons: the good one, Douglas (James Wolk), is her chief of staff, and the other is Thomas (Sebastian Stan), known as T. J., who is the first openly gay child of a president and the family’s black sheep, with lots of charm but a serious drug problem. The brothers’ careers and love lives are entwined in the continuing Hammond soap opera.


But the more entertaining moments are not family disputes but Elaine’s dealings with the president and his cabinet, a “team of rivals” that seems united in putting the popular secretary of state in her in her place.


Hollywood is usually ahead of Washington when it comes to Oval Office casting. The Fox thriller “24” posited a black president long before Barack Obama first spoke at the Democratic National Convention; “24” had a female president taking the oath of office around the time Mrs. Clinton’s supporters were selling souvenir campaign buttons on eBay. But Mrs. Clinton’s life, with all its political triumphs and private torments, turned out to be juicier than any script a movie or television studio could conjure.


And the writers, at least, don’t want that to end. “Can you keep a secret?” Elaine asks a Secret Service agent at her side. “I’m going to run for president again, and this time I’m going to win.”


Political Animals


USA Network, Sunday nights at 10, Eastern and Pacific times; 9, Central time.


Produced by Warner Horizon Television. Created and written by Greg Berlanti; Mr. Berlanti, Laurence Mark and Sarah Caplan, executive producers; Melissa Kellner Berman, co-executive producer.


WITH: Sigourney Weaver (Elaine Barrish Hammond), Carla Gugino (Susan Berg), Ellen Burstyn (Margaret Barrish), Ciaran Hinds (Bud Hammond), James Wolk (Douglas Hammond), Sebastian Stan (Thomas Hammond), Brittany Ishibashi (Anne Ogami), Adrian Pasdar (Paul Garcetti) and Dylan Baker (Vice President Collier).