Eying the multiethnic troupe of 20-somethings rocking out in the East Room to tales of the American Revolution, U.S. President Barack Obama wagered a safe guess: The Founding Fathers never dreamed of this.

The cast of the Broadway sensation Hamilton stormed the White House on Monday for a one-of-a-kind performance rich with symbolism and a touch of irony. With portraits of George and Martha Washington staring down, the singers waxed lyrical about Alexander Hamilton's unlikely transformation from impoverished immigrant to American historical luminary.

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Before the soulful singing started, Obama told an audience of invited schoolchildren he hoped the story of the country's founding would teach them that in America, what's past is only the beginning.

"That's what makes America so great. You finish the story," Obama said.

"We're not yet finished. This is a constant work in progress, America. We're boisterous and we're diverse. We're full of energy and perpetually young in spirit. We are the project that never ends."

With its fast-paced score that mixes pop ballads, hip-hop and R&B, Hamilton has hit a nerve on Broadway with the true story of the nation's "young, scrappy and hungry" first Treasury secretary.

Obama and the first lady have been major boosters of the show, in which an African-American and Latino cast play historical figures who were, of course, white.

Lin-Manuel Miranda, the show's creator and star, has forged an unusual alliance with the Obamas, who first hosted him at the White House in 2009 for a poetry-and-music event where Miranda performed what would later become the show's opening number. Obama joked that he deserved a bit of credit for the theatrical sensation, now one of the hottest tickets on Broadway.

"Hamilton, I'm pretty sure, is the only thing that Dick Cheney and I agree on," Obama quipped, referring to the former vice-president and avowed fan of the show.

Miranda and his cast, ditching their costumes for crisp suits and dresses, performed a handful of musical numbers before an audience that included Vice-President Joe Biden.

Earlier in the day, first lady Michelle Obama hosted the company for a workshop with students, telling them that of all the events at the White House, "this for me personally is the coolest."

Himself the product of an unlikely rise to power, Obama praised the show's ability to bring "unlikely folks together." He told the show's creator that he could "use the help" in Washington.

"Lin-Manuel, if you have any ideas about a show about Congress, for example," Obama said to laughter, "now is your chance."

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Lin-Manuel Miranda is seen foreground during a performance of Hamilton in New York. Miranda's hit musical about Alexander Hamilton's unlikely transformation from impoverished immigrant to American historical luminary is now a Pulitzer Prize-winner. (Joan Marcus/The Public Theater)