I took 2 exams before i left and that helped but ideally you want to get them all done.
Doing the flying in 21 days is no problem in theory but you will need good weather, instructor availability and no maintenance issues.
Its unlikely you will get a sustained period of all 3 at a Florida school so I think you will struggle.
I did it in June 2007-I lost a week to weather and my instructor left half way through my course, took my skills test on the last day. Ended up extending my stay so was there for about four and a half weeks. I did not know of anyone who got it done in 21days whilst I was there, although I've no doubt its possible if everything goes your way.
If you do it I would not recommend coming home without finishing.