Hi,
It really depends on what your comfort zone is and what very-cheap means for you.
Do you want to stay in a dorm or private room or are you bringing a tent with you? Share or not a bath? Do you need your granola cereals for breakfast and a Tropicana or a toast and butter will do? Do you want to travel from town to town hitchhiking, by a/c bus, by basic bus (with the chickens and all) or by plane? Do you plan on using the public transport in town or you prefer the taxi (though much cheaper then in the States)?
Anyhow you can say South America is still feasible on a shoestring without compromising comfort nor safety. Generally speaking adequate dorms and rooms are available in the $5-$20 range. In-city transportation is fairly cheap but obviously a bit more expensive in the capital city. So is the food item but then again it depends greatly on how tough your stomach is and how tight is your budget. A combo meal in a very cheap "restaurant" can cost $3 or even less. There is always a fast food restaurant in big cities that can help you feel closer to home if you need it for a couple of bucks!
As for beer, it is inexpensive and you can easily passout before you run out of money.
If you need something more specific I can help you out on your Chile leg. Take into account that January is the high season south of the equator therefore lodging prices tend to go up and it may sometimes be difficult to find a place to crash.
Bon voyage!
