Dollar has some deals right now, it might be worth a minute to compare.
Car Rental - Rental Cars - Rent A Car | Dollar.com Usually an upgrade from compact to midsize is only a few bucks with them, so check that size car as well
When you put in your dates, the price will show in a yellow and red box on the right side of the page. In that box there will be a link for a 'special rates on this car-click now' or something like that, so be sure to click for the lower rate.
They have some AMEX promo on their front page, but I don't have an AMEX, so I didn't look at it.
Wish, I was pricing a car for my DH and I in Vegas, and they had some good deals ($20.94/day for a compact). But that was a local rental only, not sure about dropping off in NV.