The hip-hop musical “Hamilton,” featuring a mainly black and Latino cast playing America’s founding fathers, has drawn a steady stream of boldface names since it began its sold-out run at the Public Theater in January.

The show has also attracted some more rarefied V.I.P.s: political figures with firsthand knowledge of the pressures — and scandals — that come with running the country.

Bill, Hillary and Chelsea Clinton attended earlier this month, arriving just before curtain to the surprise of audience members who had been craning their necks to glimpse Jake Gyllenhaal. Timothy Geithner, the former Treasury secretary, has also seen it, as have the former Congressman Anthony D. Weiner and his wife, Huma Abedin, an adviser to Ms. Clinton.