When I was at the CSR in 2002, I was able to buy stamps there, by the check-in area. I don't see why the other resorts wouldn't have stamps, too. Besides, how are you going to send a post card to someone bragging about your trip to WDW if there aren't any stamps to send it.
Thanks for all the info everyone! I'm going to try to get all the postcards first thing tomorrow morning and have each one signed by a character (and myself with a greeting) and sent as a holiday card to friends and family. I can't wait!