Hello Deacon,
USD 2,000 per month for two people will work if you're not a big spender and live in town with little or no transportation costs. My wife and I spent way less than that the first year here and had a fabulous time, but then again: That's quite a while ago... Rent can be anything from US 300 per month to US 1,500 per month, depending on your requirements (like everywhere else), where the 300 will give you one room with cold water only, 750 will give you a very nice place with a/c and the works and 1,500 will give you a fabulous place, but nothing to eat if your budget is 2,000...
To give you a picture of the requirements to survive here: I believe that the Immigration Authorities require proof of US 900 per person (+ return ticket) to renew the 30 days tourist visa.
With US 2,000 a month, I would say "go for it" if that's what you want. Remember: You don't need two cars in the garage and a budget for winter close (or shoes for that matter) down here.
Good luck!
AmbergrisCaye.com 
