hey bud,
three weeks is extremely short to do your private as anything can happen like wx, airplane u/s. I have finished my private in January in Daytona Beach, but I have been flying before that for a month and a half.
Make sure you have all your work down pact and know your FARs. Do you have any hours, because minimum hrs for training under Pt 63 (or 61 can't remember) is 40 hrs, 10 hrs solo, the usual xcountry and stuff.
You should contact the schools, tell them what you want, before allotting the times for your license.
I currently live in the Bahamas, and starting July to September is hurricane season so do have being wx in mind.
Hope that was a little helpful. Cheers.