IMO, you won't really need a car in Mérida itself, but it will come in handy for excursions to nearby archaeologial sites (the Puuc Hills sites, Chichén Itzá, etc.) If you have a car rented on Sunday and stay in a downtown hotel, you may not even be able to drive it - "Mérida en Doningo" sees many street closures so pedestrians can enjoy the very active scene. I make it a point to show my visiting friends Mérida on Sunday - actually, the entire weekend is very nice!

As others have advised, arrive at the airport (you already have a reservation to fall back on) and troll for cheaper car rentals. Be sure you get comprehensive insurance: Mexico follows Napoleonic Code in its laws, meaning the insurance company is your bailor, and if you do not have one, you may be presumed guilty until you can get off the hook in the case of an accident (there is no presumption of innocence.)

Also be aware theft insurance will not cover items stolen from the car (like side mirrors,) and there is no coverage available for broken windows. If you have a digicam, it can't hurt to photo the vehicle you choose as well as be sure every missing item (jack, etc.) and ding is listed on the check sheet.

And do watch the "topes" (tow-pays) - the humps in the road that may or not be well marked, especially near villages (called "sleeping policemen" in some countries.) They can create serious havoc taken at any speed at all.

You may also be able to make a good deal with a taxi driver with a decent vehicle for your automotive needs - meaning the taxi driver / owner takes the risks and buys the gasoline, you have someone to watch your goods in the car, and to be dropped / picked up by at various locations. Consider it, at least.