As most people mentioned here, nothing in aviation works as planed, at least not at this level, there's millions of things out of your hands, included, meteorology, examiners availability, maintenance of airplanes, delays with TSA processing your fingerprints, etc.. etc..
Any school that promises PPL in 3 weeks, is a school that is promising something they can't really comply with, because this also depends on how much do you study, and how good you are flying, some people need just 40 hours and other need 140, and this is something purely based on your skills.
The learning experience is lovely, so don't rush on it, enjoy as much as you can, doing it at proper timing will make you a better pilot, as you will have more time to assimilate what you learn.
If the problem is budget, then you shouldn't even considering to do it, as costs are really variable, if you mess it in a checkride (and this happen often) a re take might cost you another extra 500-1000$ so you need to have an allowance of at least 3000 or 4000 $ for non-planed things and things you might need (knee pad, strainers, torch light, charts, books, etc..)
About schools, I did my PPL in California with National Air (Don't go there!), also did some time building with Learn To Fly San Diego (lovely school!!!!) in San Diego, and IFR/CPL/ME in Florida Flyers in KSGJ (St Agustine) and I'm really happy with them!!! so I highly recommend them if you are planing FL, but as mention don't rush mate, is the worse thing you can do in aviation, if you stress your self and commit to dates due budget.