I thought you were kidding for a minute. You REALLY expect it to take less than a week for an organization to process your membership and issue you a card? You can't have very much real life experience.
If they said three weeks, it wouldn't have surprised me. Just wait until you get out in the real world.
Dennis-
Before I start, this is just my humble opinion, so take it for what it worth:
Even though the AMA is a member services organization, it still has an obligation to manage people's expectations. As you have brought up "real life experience", it is not unreasonable to expect that an online application, paid by credit card, should be able to issue a member number immediately, with no waiting period at all. If not, I would question what is being done with the information (such as receiving on the AMA end, and then someone manually processing it). There is no benefit at all for having an online system if it needs to be processed manually. My expectation, as with many other people that primarily operate in an online environment, is that things happen systematically and immediately - otherwise, I would chose to use some other medium. I chose to interact online to remove people from the equation, as it has been my experience that accuracy and timeliness improve when things are done through a back-end system and without human intervention. If that is not what's happening, they could clearly let people know up front that an online application doesn't get processed any faster than say a faxed application.
I am not saying that people shouldn't be more patient, or that 3 weeks is a long time to wait. Just that online means instantaneous to many people, and it is the responsibility of the site owner, whoever it may be, to manage that expecation when dealing with people, especially if it involves a monetary transaction.
That's all. Like I said, just my opinion! :-)