Sheehan was born in Holyoke, Massachusetts, the son of Mary (O'Shea) and Cornelius Joseph Sheehan, who were Irish immigrants. He was raised on a dairy farm near Holyoke. Sheehan graduated from Mount Hermon School (later Northfield Mount Hermon) and Harvard University with a B.A. in history (cum laude) in 1958. He served in the U.S. Army from 1959 to 1962, when he was assigned to Korea, and then transferred to Tokyo, where he did work moonlighting in the Tokyo bureau of United Press International (UPI). After his stint in the army he spent two years covering the war in Vietnam as UPI's Saigon bureau chief. In 1963, during the Buddhist crisis, he and David Halberstam debunked the claim by the Ngô Đình Diệm regime that the Army of the Republic of Vietnam regular forces had perpetrated the Xá Lợi Pagoda raids, which U.S. authorities initially accepted. They showed instead that the raiders were Special Forces loyal to Diệm's brother, Nhu, and motivated to frame the army generals. In 1964 he joined The New York Times and worked the city desk for a while before returning to the Far East, first to Indonesia and then to spend another year in Vietnam. Sheehan was one of numerous US and international journalists who received valuable information from Pham Xuan An, who was not only a 20-year veteran correspondent for Time Magazine and Reuters, but was later revealed to also be a secret North Vietnamese spy.