All the world’s a stage, all right, and never so much as when presidential politics are in play.

But reality transcended metaphor Monday when crooner-in-chief Barack Obama hit Broadway. Joining him on stage was one of the greatest actors of our time — Bill Clinton. No longer playing the role of political antagonist, Clinton is now Dean Martin to Obama’s Frank Sinatra.

No one understands better than Clinton the value of connecting with voters through the universal language of music. His saxophone performance on late-night TV when he was a presidential candidate in 1992 wowed his audience and transformed the election — and all of them since. Ever after, it seems, those who aspire to the presidency have to be musical as well as athletic.

Obama has proved himself capable of carrying a tune and has sung publicly at least twice, including at a White House blues festival, where, incidentally, Mick Jagger also performed. Maybe Clinton is playing Jagger to Obama’s Obama?

And, let’s be honest, Obama warbling Al Green’s “I-I-I-I’m so in love with you” has a different je ne sais quoi than, say, Mitt Romney reciting America the Beautiful. Speaking of metaphors …

We know these things don’t matter — or they shouldn’t — but they do. Optics. Staging. Performance. Audience chemistry. They’re all part of the packaging. Americans used to ask themselves with whom they’d rather attend a beer summit, or something like that. Now they wonder: But can he sing?

“Barack on Broadway” was perhaps inevitable for the man who accepted his party’s nomination under the stars on a stage that featured rows of Roman columns. What’s left but the real stage and, perchance, a Greek chorus?

Thus, Obama and his new sidekick appeared at the New Amsterdam Theatre, wrapping up a three-stop night of fundraisers that had included a gala at the Waldorf-Astoria and a fundraiser at the home of hedge-fund billionaire Marc Lasry. From the stage, they dazzled an audience of about 1,700, including various Broadway stars. This week, Obama returns to New York for a fundraising party at the home of Sex and the City star Sarah Jessica Parker.

OK, so there’s nothing new to see here. Hollywood likes Obama. Who didn’t know? Some like him so much that they recently ponied up $40,000 a plate for dinner with the president at George Clooney’s house.

And, yes, clearly Clinton has changed his own tune. Where once he referred to Obama’s potential “fairy tale,” he’s now a genial warm-up act. So goes politics, especially when your wife is being mentioned for another presidential run in 2016.

Destiny imposes certain adjustments.

Still, it becomes increasingly difficult for the Obama campaign to insist that the president is fighting for the little guy against the evil rich when no one is so rich as the company he himself keeps. It’s also difficult to criticize one’s opponent for running a company that made its investors rich while greasing one’s own pockets with filthy lucre similarly acquired. Bumper sticker: “My billionaire’s better than your billionaire.”

It bears mentioning that Clinton has joined Newark Mayor Cory Booker and Massachusetts Gov. Deval Patrick in distancing himself from criticism of Romney’s tenure as head of Bain Capital. Clinton went so far as to declare Romney’s career “sterling,” even though his presidency would be “calamitous for our country and the world” (no word on the tides), and warned against judging another’s work as good or bad.

“A man who’s been governor and had a sterling business career crosses the qualification threshold,” Clinton recently said on CNN.

It must be tough to play second fiddle to the man who defeated your wife (and kept you out of the White House in the starring role of First Husband). But Clinton is nothing if not a party animal, and holding Hillary’s place trumps personal pride.

Moreover, it can only help Obama to share a spotlight with Clinton. Despite peccadilloes that seem quaint compared to more recent scandals, Clinton remains not only popular (67 percent favorability), but also preferable to both Obama (56 percent favorability) and Romney (48 percent).

It is widely assumed that Romney’s campaign will outspend Obama’s, but whatever the gap, it will be minor to folks accustomed to trafficking in billions. Meanwhile, the Democratic Party’s demonization of the rich won’t wash as long as the president shares the stage with Hollywood and such billionaires are deemed acceptable.

Ain’t that a kick in the head?