For my part, I had to initiate contact to move things along. When I applied, I received a response the following day, letting me know that my application was received and to expect a response in 5-10 working days. I didn't hear anything by the end of that period and I sent a follow-up email; no response to this email by the end of the day so I contacted them by phone. The rep I spoke to finalized my application and gave me a card number. I signed in and paid (via c/card) the $15 fee and I was able to borrow books right away.
A few days later I got a response to my follow-up email, telling me that there was a back-log and I would have to wait another week for my application to be finalized. I simply wrote back to explain that everything was already handled satisfactorily.
My advice is to wait a couple of days and if you don't hear anything, definitely contact them.
(I haven't received a physical card but I don't need one so no biggie
)