IIRC, it took almost 2 months for mine. I could tell there was some intentional runaround built in to the process. ie: I had to make an appointment to sign the paperwork in front of the processor in the PD (He wasn't even a cop), and he was all booked up for a couple weeks.
Then about a month later, I was off work one afternoon and a plainclothes cop came to my house to verify my address. What if I was normally at work that day? Then around day 32, I called to follow up and was told that the processor was on vacation and don't call any more - "Someone will call you".
Oh...and as part of the process I had to go to a certified fingerprinting service (at a cost of $60 IIRC) because the local PD "doesn't do the fingerprinting". When I was called to tell me my permits were ready and I picked them up,.. guess what? They fingerprinted me!