Anyone Can Whistle was a financial failure, running only nine performances, but some critics saw it as a musical that was simply ahead of its time, and it has gone on to be a cult favorite, even though there has never been a major revival of the show. The Original Cast Recording, which was made after the show had closed, also has a strong following. Among the songs in the show are the title song, "Me and My Town", "Everybody Says Don't", and "With So Little to Be Sure Of". "There Won't Be Trumpets", a song cut from the show before its opening, has also become a cabaret favorite.
Anyone Can Whistle opened on Broadway at the Majestic Theatre on April 4, 1964, with Angela Lansbury (in her first musical role), Lee Remick, and Harry Guardino in the leading roles.