It seems to vary wildly. I sent my app in Sept 17, DPS received it Sept 22. I already had my PIN in hand as I applied online so I was able to check status easily. My app went into processing October 1 and yesterday when I got home I did the daily inquiry, expecting to see "Processing Application" for the next several weeks and was pleasantly surprised to see the status had changed to "Application Completed - license issued or certificate active". Now all I have to do is wait on the plastic in the mail which could be today or 2 weeks from now, who knows.
I have to say I was really shocked at how quick it went through, especially after having read all the horror stories of other peoples wait times. Not sure how true this is but heard that there was supposedly quicker processing for veterans, so any other vets out there, maybe it'll help speed your processing along too.
That is amazing. Perhaps you sent a nice card and flowers in with your application??
haha...