I don't think there is a reliable way to get one at the airport, but there are many 24 hour pharmacies on the strip and they all sell SIM cards. Find your nearest Walgreens or CVS pharmacy on the strip and try there.

I usually use T-Mobile prepaid, but you can also use AT&T or Straight Talk. There might be others but those are the ones I see regularly in Las Vegas. Straight Talk is a discount flat rate (I think $45 per month for unlimited usage last time I used them). So consider ST for longer trips.