I took my class in July, mailed it in August, just got it today. I'm very glad my AZ permit only took two weeks, so I've been ok to carry for a while, but now I'll be able to carry in Denver and some other places that were off limits. When I called a month ago to check they told me the background check had just come back. They were so backlogged they had to send the prints of to Santa Fe for background checks.
From what I hear this is typical here.