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Arena Stage’s new musical Dave may not be The Presidential Play We Need Right Now (hell, it’s not even The Movie Adaptation Anyone Asked For, Ever), but it’s more fun than it has any right to be.

Politically, this comedy about an accidental commander in chief is neither cutting and insightful nor weightless and playful, but holding to the middle ground allows it to come at you from its own personalized blindside. It disarms with well-constructed melodies and lyrics, better-than-the-film jokes, and performers who are visibly having fun. Vote Dave!

Those who recall the 1993 movie starring Kevin Kline and Sigourney Weaver know that Dave Kovic (Drew Gehling) is a history teacher who moonlights as an impersonator of President Bill Mitchell because he needs the money — and because they look exactly alike. One night he’s called upon by the White House to serve as an official double, complete with Secret Service detail, to draw attention away while the real president boinks his staff secretary. But uh-oh! Mitchell has a stroke in flagrante delicto, and his evil chief of staff (Bob Alexander) and in-over-her-head communications director (Susan Lee) install Dave at 1600 Pennsylvania Ave. as their puppet. It’s a comedy d’etat.

But like I said, from this preposterous (arguably treasonous) setup, a surprisingly winning story is told. As directed by Tina Landau, who recently debuted the SpongeBob Squarepants musical, Dave thankfully doesn’t think it’s a lot smarter than it actually is — and it’s not half-dumb. It’s not trying to change the way you think about politics, but it’s happy to mock the system’s sillier aspects. One of my favorite digs is a bit mocking Panda Diplomacy: The Chinese have sent the National Zoo a new one, we’re told, “probably as impotent as his predecessor.”

Gehling, who resembles no real-life president but instead House Speaker Paul Ryan, leads a promising ensemble, most of whom are making their Arena debuts. His desire to be the best fraudulent president he can be drives the play’s plot.

He gallantly steps in at a baseball game to help a young national anthem singer who has forgotten the lyrics — right at “gallantly,” in a charming grace note. He challenges a pack of high schoolers to a race: “Last one to the White House has to pay for Medicare!” And, of course, he slowly wins over the embittered first lady (Mamie Parris), including backing her “eldercare” initiative. Gehling, Parris, Lee, and Alexander are all, speaking on the record, worthy of reelection.

On the tech side, a few things with this show are far from perfect. The set of revolving, curved panels/video screens is amusingly reminiscent of a CNN soundstage, but perhaps too large for the space we have here, leaving scant room for choreography. Like a politician, its ambition might have it already dreaming of a bigger office. And do we really need the all-caps projections announcing each setting? LINCOLN BEDROOM — cool, thanks. OVAL OFFICE — uh, yeah, we know. Even an ASSISTED LIVING facility — really?

And the makeup needs to up its game, too. The foundation line on the first lady’s forehead is so stark, county police would hesitate to cross it.

But with a book (from Thomas Meehan and Nell Benjamin), lyrics (Benjamin again), and music (Tom Kitt) like this, it’s easy to forget the makeup. Not every song is a winner — please cut “Presidential Party,” and not just because John Quincy Adams deserves better — but most are enchanting. I’m haunted by the scene in which Parris’s Ellen Mitchell compares her relationship with the president to a magic trick: You stabbed me full of swords, she says, and to great applause. And the dialogue, right through the last scene, is laugh-out-loud funny.

Going on now through August 19, Dave is the summer treat no one saw coming. It doesn’t take itself too seriously, and any musical that points out that even Lincoln trampled the Constitution and suspended habeas corpus must be doing something right.