Stephenson was born in DeFuniak Springs, Florida in 1944, and grew up in nearby Pensacola. He attended Pensacola High School, and he earned All-State accolades as a quarterback. He accepted an athletic scholarship to attend the University of Florida, where he played for coach Ray Graves from 1964 to 1966. His arrival on the Florida campus coincided with that of another standout recruit, Steve Spurrier, who became the starting quarterback in 1964, and who won the Heisman Trophy in 1966. Stephenson remained a backup.
Stephenson graduated from Florida with a bachelor's degree in physical education in 1967.
Professional football coaching career
After serving as a quarterbacks coach the previous season, Stephenson succeeded Chuck Knox as Buffalo Bills head coach on February 3, 1983. Stephenson was reportedly surprised to get the job, claiming that Bills owner Ralph Wilson "never explained his reasons for selecting me." Under Stephenson, the Bills went 8-8 in 1983, 2-14 in 1984, and after they lost their first four games in 1985, Stephenson was replaced by Hank Bullough. Perhaps the most lasting impression that Stephenson left on the Bills was changing their helmet color from white to red prior to the 1984 season, insisting that the change would aid Buffalo quarterbacks in finding receivers downfield. At the time, three of the Bills' four division rivals, the New England Patriots, Indianapolis Colts, and Miami Dolphins, wore white helmets. The gambit didn't work as interceptions actually increased the subsequent season.