Anita Gillette went on to have a long career, that's still going, most notably in a few episodes of 30 Rock as Liz Lemon's mother. She had a successful career on Broadway, even getting a Tony nomination in Neil Simon's Chapter Two. (Though she wasn't in the original casts, she appeared in the Broadway companies of Cabaret and They're Playing Our Song.) She also did a ton of TV, that included a semi-regular role on Quincy, ME and lot of games shows. (She was on The New $25,000 Pyramid 53 times) And when they made a series out of the film, Bob & Carol & Ted & Alice, she starred as 'Alice.'
Mr. President opened in October, 1962. It wasn't a significant success, though it ran for 265 performances. The show is a bit old-fashioned, as Broadway was slowly beginning to change (that was the year of A Funny Thing Happened on the Way to the Forum and Stop the World - I Want to Get Off), but it has quite a few enjoyable songs, including this one.