I suppose it varies by county and sheriff as to how quick you get it here. Mine took about 2-3 weeks for my MN permit. My Utah permit took considerably longer, between 2 and 3 months.
You are correct on the sheriff comment. I am lucky to live out of the city limits and fall under the Sheriff's jurisdiction. I have always gotten along well with out County Sheriffs. I even have his cell number in my phone. Many Sheriffs don't like doing the paperwork, and a couple hate carry permits, so they drag their feet. Our local Chief of Police, and a very good friend of mine, does not like permits and hates to approve them, so he will put them on the "to do" stack and stall.
An interesting thing in Minnesota is that the fee, by law, is actual cost of background check with a maximum of $100, and the renewal is the same with a max of $75 (I think). The strange thing is that everyone charges $100 & $75. A few have tried to charge $100 for renewal, but they have been called on it by applicants - typically instructors.
My Utah permit took just under six weeks from the date I put it in the mail until I had the card in hand.