I expect a similar process to occur with Crist -- he could well attempt to position himself as a 'leftist' candidate in primaries.
Not in a primary. Since he'd be running against someone like Alex Sink or Nan Rich, they'd have an immediate boost among the South Florida liberal group. Far better for Crist to focus on the groups he wins with - African-Americans, teachers, Tampa Bay, and conservative Dems. He needs to stay relatively conservative to hold onto the Blue Dogs, while still reaching out to African-Americans, where he's been traditionally strong, and teachers, who love him.