Okay, this sucks.
I was expecting my iPhone activation to take less than three minutes and that I would be playing with my iPhone right now. Unfortunately, I'm getting a message from iTunes saying "Your activation requires additional time to complete". After talking with AT&T iPhone activation support, I learned that this process could take up to six hours and that there's nothing I can do to speed it up.
Since I can't do anything with my iPhone (except call 911) until it's activated, this is the equivalent of opening a Christmas present and then being told you can't use it.
Update: Activation took 7 hours.