Annunzio, an Italian-American was born in Chicago, where he remained for his entire childhood and much of his adulthood. He attended Crane Technical High School and DePaul University. He then had careers and high school teacher and labor leader. In 1964 he was elected to the United States House of Representatives from a district in Chicago as a member of the United States Democratic Party. He was reelected 13 times and served from 1965 to 1993, deciding not to run for reelection in 1992. He was chairman of several committees including the House Administration Committee during his later terms in congress, and was particularly notable for serving on a subcommittee for consumer affairs. In 1989 he urged people to burn credit cards in order to drive down interest rates and stop themselves from going into debt.