Nussbaum was born to a Jewish family. His acting career started in the 1950s. He appeared in many of David Mamet's plays both on and off Broadway, as well as in Chicago. His films include Field of Dreams, House of Games, Things Change, Fatal Attraction and Men In Black.
In 1997 he received a Jeff Award for his performance as Reverend Lionel Espy in David Hare's Racing Demon. His performance in Mamet's Glengarry Glen Ross on Broadway received a Drama Desk Award in 1984. As a Director, his work has included Where Have You Gone, Jimmy Stewart? (2002) by Art Shay.
