In Maine, the law reads: Within 30 days for a resident of 5 or more years, otherwise it shall be issued within 60 days.
For myself going through the local city police chief, it took around 8 business days. Three months later for my boyfriend through the same municipality, it took 4 days. The shorter turn-around time might have had something to do with his getting a background check done two months earlier so that he could go through the Maine Law Enforcement Pre-Service Program, but that's just a guess on my part.