Thanks for all of the responses. I finally discovered what I think may have been the answer on another thread. Apparently, if you booked through a non-Disney site (like an OTA), AND the people in your room do not all share the same last name, your Magic Bands can get stuck in a hold status.
To fix the problem, I called the website support number listed on Disney's help center page. I selected option 3 (for technical enquiries), and then waited for about 15-20 mins. I explained to the CM that I was receiving the "Act quickly. Your order may ship at any moment" message, but other people with whom I am traveling (different rooms/different reservations) had already received their magic bands. I then told them that I had read on disboards that there may be a problem because I had booked via an OTA and the people in my room have different names. After checking on our customization status, she came back and confirmed that the bands were on "hold". She was able to have the hold removed. The CM said that they should ship in the next day or so!
Apparently, some people call and the CM tells them the bands will ship 10 days out. Don't wait! Call the website support number and ask them to check to see if there is a hold on your bands.
Hope this helps anyone else who is running into the same issue!