From what I've been reading over the past couple of months it's highly unlikely you will complete the PPL in 3 weeks (FAA or JAA). This isn't to say that it's impossible but it's risky business budgeting for only 4 weeks. The worse that could happen is you'd have to head home with only 20-30 hours
Think bad weather days, maintenance issues, instructor days-off, instructor / student illness (it's happened) etc.
I'm hoping to head out to Florida in October (JAA PPL) and will be budgeting for approx 6-8 weeks but still wonder whether this is enough to be safe.
Good luck.