From a police standpoint
In New Hampshire, the law states that a Pistol/Revolver Lic. shall be issued within 14 days of application. The OP is part of the reason why this can take some time.
So...to clarify....at our little PD at least this is the way it usually goes.....
Someone will stop by and get the application from us. We give them a basic "crash course" on what they can/can't do with the permit. Once the paperwork is in and completed, that will start the ball rolling.
I put the application in my Chief's box (he's the only one that can issue them for our PD) and he starts his end of the paperwork (which he may/may not get to in short order depending on how busy) INCL. AN APPLICATION TO THE COUNTY/STATE FOR A BACKGROUND CHECK.....postage paid, mailed out, and thus starts the delay for days and days. The county will mail/relay the check back to us (who knows how long this can take?!?!:banghead
Once they complete the process, then the Chief still needs to draft the permit, contact the applicant, get them to come back to the office and SIGN IN PERSON the permit......
This is a very rough example of "how it goes".....so depending on what state you live in, and the laws that are in place, you may just be waiting for a while. Ahhhh....the wheels of justice do INDEED turn slowly. As long as we are within the 14 days here we are safe! Hope this helps!