McKeever was born in 1918, and attended Episcopal Academy in Pennsylvania, graduating in 1935. After graduating he joined Cornell University in New York, being one of the top freshman players. He made the varsity team the following season, and was given a letter.[3] In the first seven games of the 1936 season, McKeever was a starter in all but one of them.[4] He was a top player on the Cornell team, and earned letters in each of his three seasons on the varsity squad.[5] McKeever was named first-team All-American by Grantland Rice following the 1938 season.[6] He was an inductee into the school's hall of fame in 1978.[6]