It's wildly varied by country, urban vs. rural, etc.

Here's an excerpt from Legal Nomad's amazing and life-changing world travel resources page:

• "Brendan from Brendan’s Adventures has budget breakdowns for Bolivia andArgentina.
• Kim from So Many Places breaks down her travel budget for Ecuador.
• Keith from Traveling Savage on how much it cost to travel in Argentina.
• David from Go Backpacking on the cost of travel in Colombia.
• Thorough, detailed budget breakdowns for Central America, divided by country and type of expense, from Jeff of Lengthy Travel.
• Neverending Voyage’s budget breakdown for Brazil, Argentina and Paraguay and forBolivia and Peru, as well as their full budget for 1-year in South America.
• Alex from Alex in Wonderland on 2 weeks in Honduras (including diving costs).
• A different Alex (from Virtual Wayfarer) on 21 days in Argentina.
• South American budget breakdown (very detailed) from Jeff of Lengthy Travel
• The Globetrotter Girls on how much it cost them to travel through Central America."

Hope that helps!

I just got back from a 12 week backpacking trip around some of South America (Peru, Argentina, Chile and Uruguay).  I have been to SEA before and was hoping the cost would be around the same, but now that I am back I have to say South America seems to be a little more pricey than SEA.  However it all matters what countries you are going to, for me Peru was the cheapest and the other three where about the same. Here are some prices, all in USD.

Food-I cooked a lot in my hostels because it does not cost much money.  I could make a meal for about $2.  In Peru you can get a set meal at a restaurant for about $2-$4.

Hostels-I only stayed in dorm rooms and payed from any where from $5-$12, with most times right around $8.

Transportation-I did all my traveling by bus because it can cost a lot to fly.  Bus tickets seem to be what I spent the most money on.  In Peru it seems like it is about $1-$2 per hour.  Argentina and Chile it is more like $3-$4 per hour.

Over all I lived on $30 a day (that is with bus tickets and everything besides my flight to get to South America) and it was not to bad of a budget.  You just have to keep track of everything because if you go out a lot money seems to fly away.  The reason why I think SEA can be cheaper is because it has more choices for buses and all that.  Where in South America I feel like there is not as much of a dirt cheap way to go.  Hope this helps you.

I've literally just written a post on it: http://www.coffeewithasliceoflife.com/2014/10/04/how-much-money-do-you-need-to-travel-6-months-in-south-america/ Its a lot cheaper than you think. I spent much less than in Asia.

It isn't extremely expensive.  I'd be a little leery of backpacking through Venezuela.  On the border of Columbia, you have to worry about FARC (a semi-terrorist organization).  I'm also not sure that they are completely over the violence from a few months ago.

Prices in the grosery stores a bit higher than in New York. 

Only local stuff like rice, chicken and sugar and alcohol are cheaper.