The hardest thing about getting my PI was the waiting. You have to be ridiculously patient. As for how long it takes, it really depends on the internship.
The Animal Programs people found out in Sept/Oct for the PI that started in January. That just killed the rest of us when we were waiting!
Most found out around mis-November, as I recall, for my PI beginning in January. Some didn't find out until December! Unfortunately, Disney doesn't worry too much about the fact that their hopefuls need to make other plans in case they're rejected! The good news is that the longer it takes, the more likely you are to be accepted. (Doesn't mean you will be accepted if it takes a long time, but the chances certainly go up. They reject people as quickly as they can)
Hope this helps! Sorry I don't have a "magic day" that you'll find out. You'll just have to concentrate on patience. Or cookies. Or something else that awesome and entirely unrelated! *pixie dust*
