Give it a few. I submitted my AMCAS and got an e-mail:
"The Medical College of Wisconsin (MCW) recently received, from the AAMC, your results on the April 2006 MCAT. In reviewing your scores the Committee believes that should your other academic and supporting credentials complement these scores you may be a competitive candidate in the application process for the entering class of 2007. I would like to introduce you, as a Wisconsin resident, to this premier medical school located virtually in your backyard. "
Took a couple of days (some say up to a week.) Then about two weeks later you get one like this:
"We have received your AMCAS application and are pleased to learn of your interest in the Medical College of Wisconsin (MCW).
We are happy to offer you the opportunity to complete our on-line secondary application. Prior to completing"
Anyway, hope that helps for the timeline...best of luck!