George M. Cohan, the “man who owned Broadway” in the first two decades of the 20th century, was a terrifically volatile character: vain, ruthlessly ambitious, pugnacious. By the time he was in his teens, he was bossing his own parents around in the family vaudeville act. An uneducated poor Irish kid, he came to Broadway in 1901 to battle the operetta with slangy popular songs – and won. Cohan became a millionaire, but even in success, he was famously vindictive – when out-of-town critics gave him bad reviews, he would refuse to play their cities the next year.

Given the richness of Cohan’s life,it’s mind-boggling that the Irish Rep’s new Cohan musical manages to make him – dull. The most exciting thing in the paint-by-numbers “George M. Cohan Tonight!” is its exclamation point. Cohan – who ought to bristle with energy – is presented by playwright-director Chip Deffaa as a sort of Irish Lawrence Welk, mildly introducing one Cohan song after another. Despite the song-and-dance talents of Londoner Jon Peterson, who plays Cohan, “George M. Cohan Tonight!” feels like middling cabaret without the cocktails.

The very concept of a one-man musical is mystifying. With all that uninterrupted hoofing, singing, and talking, when is the man supposed to breathe? And no intermission, no less. The scarcity of oxygen inevitably affects Mr. Peterson’s volume; occasionally he cannot be heard above the snappy three-piece band. A winded star trying to finesse a gulp of water seems poor stagecraft in such an intimate space; at times, you can feel the audience wanting to offer the poor man a break.

To his credit, Mr. Peterson tries to wring something out of the tired material; his unflagging energy goes a long way toward propping up the book’s droopy arc. He dances well, he sings well, and he gamely tries to carry off the creaking monologues. It’s not easy to deliver lines like “Harris is to become one of the only people I ever allow to get close to me” without sounding like one of those museum audio guides, but he gives it his best shot.

Mr. Peterson has a warm, unpretentious singing voice, which – along with Cohan’s catchy rhythms and sentimental melodies – often charms the crowd. It’s worth noting that these renditions have nothing in common with Cohan’s own gritty, brassy interpretations of his songs. But Mr. Peterson softens all his edges; ultimately, his Cohan is a sort of all-American (though part Irish) song-and-dance man with a heart of gold.

Thing is, that’s not Cohan. The man was a megalomaniac. Mr. Deffaa relates an anecdote from the end of Cohan’s life, in which, after seeing his biopic, he turns to his son and says, “My God! What an act to follow!” The bit is played as if Cohan were the sort of nice old man who made self-mocking jokes about his own puffed-up ego. On the contrary, I expect that Cohan’s gargantuan ego devoured everything in its path.

Most disappointing of all is the play’s easy touting of Cohan’s patriotism – as if the intervening years had yielded no critical distance at all. Cohan, we know now, was likely not born on July 4, as he so often claimed. His vaunted patriotism was also his bread and butter; he learned early on in his parents’ vaudeville act that a flag-waving bit always got a round of applause. And the author of “Over There,” which supposedly sent young men running to enlistment offices, did not himself venture “over there.”

The only thing here that feels like Cohan is the music.The songs – corny, rousing, without a smidgen of subtlety – are great popular songs. Classics like “Yankee Doodle Dandy” and “Mary’s a Grand Old Name” could only have been penned by Cohan. In Cohan’s songs one glimpses constructions and ideas that were to emerge again and again in Broadway shows. Cole Porter’s “Kiss Me, Kate” is ripe with the echoes: “Always True to You (In My Fashion)” is a descendant of “I’m True to Them All,” and “Another Op’nin, Another Show” harks back to Cohan’s “Give My Regards to Broadway.” “Mary’s a Grand Old Name” is a forerunner of Leonard Bernstein’s “Maria,” and all those show tunes that spell out words have a hint of “Harrigan” in them.

Because of his crude ambition and fearless vision, Cohan’s talent made a mark on American theater. It’s curious that a show about his life should make the mistake of playing it safe.

Until April 23 (132 W. 22nd Street, between Sixth and Seventh Avenues, 212-727-2737).