An outstanding two-sport athlete, Sponheimer won letters in football in 1966, 1967 and 1968 and in varsity basketball in 1966-67. He was an Associated Press All-America honorable mention selection as a defensive tackle in 1967 and 1968. Sponheimer was also a two-time All-Ivy first-team pick. He was selected to the AP All-East second team in 1967 and received AP All-East honorable mention as a senior. He was named to the Ivy League's Silver Anniversary All-Star football second team, as selected in 1981 by sportswriters, broadcasters, and the league coaches and administrators. Sponheimer was a center on the varsity basketball team as a sophomore. He was drafted in the 10th round of the pro football draft by the Kansas City Chiefs of the AFL in January 1969.
