If you found a job anywhere it would be "off the books" (in black) here unless you have residency of some sort. It's possible to find such jobs, though there aren't a lot and they don't pay well and usually require a lot of hours to make any money. You might be able to count on another $300-$500 USD a month with such a job IF you can find one, but that much money would probably require it to be fultime (which could be as much as 7 days a week). And don't count on tips in the bar scene, or at least not very much.
I know many people who live on around $7000-$8000 pesos a month, but they are used to living very poor. They live in bad (or at least not-so-good) neighborhoods, usually outside the city with between one and two hour rides into the city for work, or they live in pensiones (hotels) in the city (and often in not-so-good neighborhoods), which are small usually single rooms with maybe a bed, maybe a dresser and maybe a table, with a shared kitchen and bathroom down the hall. There are also hostels, but I don't know much about them.
So you could live on $1200 USD a month (would be about $15,000 pesos if you get the blue rate - an absolute must, or as close to it as possible, if you are trying to save money - otherwise at the official rate it would be about $10,500 pesos, which is a serious cut and you wouldn't be so comfortable) even living in a small studio apartment. I think Cecil's numbers are accurate, so do the math and see how you feel about it. If you can find even cheaper places to live (I know a couple of students from Sweden who are sharing an apartment for about $600 USD, i.e., $300 apiece, per month, though it's a one bedroom) you can have a bit more comfort. If you can find a job, you can have even a little more comfort. It all depends on what level you are willing to live.
You do not want to bring money in by using ATMs or using foreign credit cards (official rate + fees). If you don't have cash in your hand, you have to think about getting money in via Xoom or other money transfer places and then you start talking about worse than blue rates, but better than official rate - but a loss of that difference between Xoom and the blue rate. Or you can go to Uruguay and get USD out of ATMs and bring back here to change at the blue rate, but it costs quite a bit to go there via boat across the bay for just a money run trip (and again you are losing money from your ideal rate).
Make sure you know what you're getting into and understand about the currency exchange rates and know how you will get your money down here. That is probably the biggest challenge that everyone who lives here and gets their money from outside the country has to face, sometimes on a weekly basis. Then there's the 30-40% or so inflation and a blue exchange rate that doesn't keep up with inflation, so your buying power with the money you have will likely be going down over time.