During my TP-run last summer I booked the Hard Rock Hotel in Vegas (~$12/15 cab from the airport) via the American Express travel website for £35 and according to the booking conditions I did not have to pay the resort fee:

Resort Fees
-$22.00 + 12% tax per room/night Resort Fee - FOR DOMESTIC USA CLIENTS ONLY to be paid locally by guest.

On checking-in, the agent began to inform me of the fee and then stopped herself, before telling me about having had an upgrade to a corner suite (which was massive), sadly as I was to be resident for less than six hours thanks to an earlier mis-connect at LAX it was somewhat wasted on me.