Figure USD$2000 month. No reason to come here if you want to live like a backpacker - the plane ticket alone is going to cost you ~US$1000. A nice place in Palermo on a temporary basis is going to be around USD$800/month - short term rentals are always priced in USD, although it's nominally illegal.
If you're coming for 3 months, bring USD in cash and change it as you need - the exchange rate really is that volatile, it's 10 pesos/USD now, but could be 12 in a month, or 14 in two, depending on how heavy government manipulation is (the government actually manipulates the black market rate as well).
I've mentioned xoom.com before - if you do run out of USD cash, you can always transfer money to yourself with that service (it's a western union clone) for a slightly less favorable rate, but still worlds ahead of the official exchange rate.
http://xoom.com/argentina/fees
Some things are much cheaper than the US, some are more expensive. The higher end is a much better deal than trying to live on a budget. Groceries etc. are actually relatively expensive here right now (seeing tomatoes at +25 pesos/kilo in verdularias), but eating in some of the best places in the city (molecular gastro etc.) is still around US$50/person with wine. I'd spend my time at those places, at closed-door restaurants, private parties, etc. Cocktails at decent places are still cheap, 50-75 pesos is normal (Franks, Ferona, 878 etc.). Beer and wine are cheap. Buses/subways/taxis practically feel free they're so cheap, Romania style prices. I think cross-fit is around 500 pesos a month for 3x/week if you're looking for that, but I haven't been since May, so it probably has gone up.