Actually, the AMA *did* manage my expectations when I applied last month. First of all, the online application is "courtesy of District VIII Web page". I take this to mean that National hasn't spent the time and money to put the functionality into their web servers. After submitting the application, the followup page states that it will take about a week.

I am an impatient type as well and as soon as I saw the charge on my CC (online, of course), I called the AMA. Jeff Hoover was very nice and told me my number over the phone. I then printed the member verification page.