Merida is an amazing little town packed with full with history. It is well worth 1,5-2 days of your time. I guess if you plan everything carefully or if you drop some of the smaller things you can cram it into 1 day.
I would recommend to buy an "entrada conjunta". This combi-ticket is much cheaper than paying for the entrance of 2 or 3 sites seperatly. With this ticket you can see:
-Zona Arqueológica de Moreria
Together with the ticket you get a little booklet with some additional information on the more important sites. In the booklet there is also a little map indicating all the historical sites and museums in town, and there are quiet a few. When I was there, in 2007, I bought the ticket for 6 euros but that was the cheaper version because I had my student card with me.