I have never had any trouble spending US money in Cozumel. I try to use credit cards as much as possible. I would make sure that you have smaller bills because you may receive mexican money as change. I hope this helps!
Swakman...actually $2 US dollars would be close to $20 mexican pesos at a 1x10 exchange rate. I found it is best to change money because using credit cards you really don't know what your exchange rate will be until you get the bill. Dollars do work, but the stores don't give as good a rate as the money exchange place. The best rate of exchange I have found is an American Express office on the ground floor by Punta Langosta (the cruise ship pier downtown)