Sheehan was born on August 23, 1940, in Somerville, Massachusetts. The son of Irish immigrants, he is one of seven children. He graduated with a B.A. degree in English from Boston College in June 1962. After graduation, he was commissioned a second lieutenant in the U.S. Marine Corps. As a captain, Sheehan was awarded the Silver Star Medal for gallantry during combat operations from September 14 to 17, 1968. He holds an M.S. degree from Georgetown University in Government. His professional military education includes the Amphibious Warfare School, Naval Command and Staff College, and National War College.