After enjoying success at the college level, Budd was drafted after his senior year by the New York Knicks in 1960. He was the 10th overall selection in the second round (at the time there were fewer teams in the league and each round only had eight selections). He was drafted the same year that Oscar Robertson and Jerry West were picked No. 1 and #2, respectively. Though never an All-Star, Budd did enjoy moderate success while playing at the highest level. One of his claims to fame was that he was one of the three centers for the Knicks that attempted to guard Wilt Chamberlain on the night of his record-setting 100-point performance. On that night, Budd was the only opponent who mustered a double-double, scoring 13 points and grabbing 10 rebounds in 27 minutes. Also on that same night, Budd was the only other player in the game to collect a double digit number of rebounds (Chamberlain had 25). Budd is the only person from Woodbury, NJ to ever play in the NBA, and wore No. 10 as his jersey number.