For Clark County 120 days, maybe 118 or 119. Strange thing is that the issue date on my card is only a few days after the day I applied for it. Of course it works out better for the state/county that way as it makes it is closer to my birthday on that half of the calendar than when I actually got it.
I personally have my suspicions that the Sheriff has instructed the CCW detail to wait as long as possible before sending cards out. No other counties take nearly as long. As for time for background checks, it's all done pretty much instantly with computers. I've seen folks in other counties report getting them in a couple weeks.
The argument the Sheriff's office has is that there is a large number of people applying. Non-sense. Clark County has more personnel to handle CCW than other agencies. Besides, why would my issue date be a few days after my application date and I didn't get it until after 118 days?
Looks like it's time to elect a new Sheriff who doesn't pull this kind of crap.