A very important, and I think very modern film at the time, After the Bay of Pigs, JFK's assassination, and other events, presidential politics and world conflict was very in vogue in 1964, When "May" was released. Ironically, just the month prior to "May's" release, Dr. Strangelove had opened, satirizing the whole shebang.
I too was a Martin Balsam fan. He was in so many great pictures, but two favorites that come to mind are 12 Angry Men, and his memorable role as Detective Arbogast in Psycho.