After graduating from high school in 1971, Morse studied acting at the William Esper Studio. He began his acting career in the theater as a player for the Boston Repertory Theatre in the early 1970s. In the mid-1970s, Esquire Jauchem, artistic director of the Boston Repertory Theater, adapted and directed a stage musical version of "The Point!" that starred an 18-year-old Morse as Oblio. The production later toured to the Trinity Square Repertory Company in Providence. He spent some time in New York's theater community in the early 1980s before moving into television and film. During that time, Morse was listed as one of the twelve most "Promising New Actors of 1980" in John A. Willis's "Screen World, Vol. 32". Morse's big break came in 1982 when he was cast in the television medical drama "St. Elsewhere". He played Dr. Jack "Boomer" Morrison, a young physician who is forced to deal with the death of his wife and the struggles of a single parent professional.