Hi Katie,
I was in the same position you are coming into. I arrived here in September 2012, took the TEFL for a month, and then went job hunting in October. My TEFL teachers told me it would be so easy to get a job, but it was miserable and no one was hiring! Luckily I had some savings and with Xoom, you can almost get the blue dollar rate! For me, the jobs started picking up in January. I just applied to everything everywhere and things started to come around. Now its March and I am already set for jobs and am turning things away. I make more than enough to live teaching private classes and working for an institute and I also have time to volunteer and take spanish classes (which are in payment for the volunteering). I'd say not to plan on saving much, but its possible and I know some people who are able to save a little on a teachers salary. And we all still go out, eat out, and live in nice places in Palermo. We definitely are not scraping by! Its just a matter of finding the right jobs, which can take a while.
I'd say if you come in October you should expect to find issues finding jobs. To live each month, you would need about 3500-4000 pesos, so if you can swing that in savings then, go for it! But if not, then maybe it would be safer to come in January. Its also just a love for the city though. I really like living here and have found that everything seems to work out in Buenos Aires, one way or another. Just maybe not the way you thought.