A similar scenario is playing itself out all over again, this time over the California governorship. Beatty's fellow screen actor Arnold Schwarzenegger is just over a year away from standing for re-election and, despite a euphoric rise to power and an uncannily long honeymoon, is now struggling with rock-bottom approval ratings.
For months, the media has been fantasising about a Beatty-Schwarzenegger match-up - Bulworth versus the Terminator - mainly because it offers an opportunity to discuss the two men's glamorous lifestyles and famously expansive experiences with the opposite sex, instead of having to focus on the grey minutiae of state politics.
A little surprisingly, the 68-year-old Beatty has taken the bait - sort of. Last Thursday night, he popped up as the keynote speaker at a nurses' convention in Oakland, outside San Francisco, and proceeded to rip into the Republican governor for his attacks on public service workers. (Infamously, Schwarzenegger said of nurses at the beginning of the year that he hoped to "kick their butts" - a remark which at a stroke demolished his superstar aura and turned him, in the public's mind, into just another lousy politician.)
"Government is not show business," Beatty told the crowd. "Government by show, by spin, by cosmetics, by photo ops, by fake events, by fake crowds - that's a mistake." Then he laid into Schwarzenegger for the "insulting and bullying" attacks the Governor had made on the nurses, fire-fighters, teachers and other unionised public workers and said the state had to take care of those who took care of others.
The crowd lapped up his every word. "Run, Warren, run!" they chanted. On that topic, though, he was his usual enigmatic self. "I have a day job," he pointed out. Pinned down by reporters after his speech, he did not rule out running for governor, saying only that now was not the time to talk about it.
This was Beatty's second political speech in recent months, following a very similar tirade at the University of California at Berkeley in May. On that occasion he explained that he usually found it hard to criticise the politics of his fellow actors, even those on the right, but that Schwarzenegger's failure to come to grips with California's dismal public finances and his attacks on public service workers prompted him to speak out.
Although Beatty has never run for public office - he has merely played politicians in the movies, most notably a renegade California senator in the 1998 political satire Bulworth, which he both wrote and directed - he has been actively involved in the Democratic Party since the Vietnam War.
As a man of enormous personal charm, he certainly has the outward personality to carry off a high-profile candidacy. His womanising past is unlikely to count against him, since he has been happily married for years to Annette Bening, with whom he has four children. (Besides, Schwarzenegger was no choirboy in younger days either.) Those who know Beatty say the reason he never plunged into electoral politics was that he felt he had too much to lose if he failed.
Could it be he has changed his mind about that? Or is it more likely he is once again flirting with the media, this time to help to defeat a flurry of controversial special anti-union ballot measures being sponsored by Governor Schwarz- enegger this November? Either scenario is possible.
For the moment, the most promising conventional candidate who might represent the Democrats against Schwarzenegger next year is state treasurer Phil Angelides, a man who wins wide-spread praise for his intellect and his grasp of policy but who enjoys marginal name recognition at best.
Beatty is certainly known to one and all. But opinion poll respondents say the Schwarzenegger experience has made them shy of celebrity candidates. Can they really mean that? Does Beatty really mean what he says? Only time will tell.