Tate Casey came close. He was a pitcher for the 2005 UF baseball team that was runner-up to NC Texas that year, and a TE on the 2006 and 2008 NC football teams.

Cornelius Ingram also came close. He was on the 2005 basketball team, but not the 2006 team that won the NC, and a TE on the 2006 and 2008 NC football teams.

Jeff Demps was on the 2008 NC football team, and on the 2008 track & field team that finished second by 2 points for the National Championship. Ironically, Demps was on the 4x100 relay team until he got injured; and that team, with an alternate, ended up still winning the NCAA National Championship for that event... if he hadn't gotten injured, he'd have been on the winning team.

So, 3 guys that came close, but no cigar.