Spong was born in Portsmouth, Virginia and attended the public schools as a youth, and later Hampden-Sydney College, the University of Virginia, and the University of Edinburgh in Scotland. He studied law, and was admitted to the bar in 1947, commencing practice in Portsmouth soon thereafter. During World War II, Spong served in the Army Air Corps, Eighth Air Force from 1942 to 1945. After the War, Spong was a lecturer in law and government at the College of William and Mary from 1948 to 1949.

Spong entered Virginia politics as a member of the Virginia House of Delegates from 1954-1955, and afterwards as a member of the Virginia State Senate from 1956 to 1966. While in the Senate, Spong was chairman of the Virginia Commission on Public Education from 1958 to 1962.

In 1966, Spong was elected as a Democrat to the United States Senate for the six-year term commencing January 3, 1967. He was subsequently appointed by the Governor of Virginia on December 31, 1966 to fill the vacancy caused by the resignation of A. Willis Robertson for the term ending January 3, 1967. Spong served in the Senate from December 31, 1966 to January 3, 1973, and was an unsuccessful candidate for reelection in 1972. After his Senate career, Spong returned to the practice of law, and also served as a law professor and the dean of the Marshall-Wythe School of Law at the College of William and Mary from 1976 to 1985. He was appointed interim president of Old Dominion University in 1988, and was a resident of Portsmouth until his death. He is interred at the University of Virginia Cemetery in Charlottesville, Virginia.