For some reason, Miami-Dade County went for Clinton that year by only 4%, while it went to him by 20 in 1996. Maybe Cuban-Americans were still almost monolithically Republican in 1992, but warmed up to Clinton a little four years later.
Also, Florida went to Bush by 22% in 1988, so there was still a lot of ground to make up.
This, plus the state was strongly Republican-leaning since the 1950s. Even LBJ only won 51% in 1964, as did Jimmy Carter in 1976.
I wonder whether Reubin Askew, Bob Graham or Lawton Chiles could have won the state in a presidential election.