We did BA-Iguazu-Patagonia in 12-13 days and it felt okay. Of course, you could spend more time in any place, but that itinerary shouldn't feel too rushed.

We spent 3 full days in Iguazu -- more than most people do -- but we thought it was time well spent. We went to the Argentine and Brazilian sides and then spent a day biking on the trails near the Sheraton and lounging around. I guess it depends how much you like nature and waterfalls. You could do Iguazu in 1 day, but I think that would feel very rushed. And personally I find it a bit harder to get the ambiance of a spectacular natural area when it's sandwiched between 2 plane flights Your opinion may vary.

For Patagonia, you could spend a few days or a month. I would HIGHLY recommend that you see the Perito Moreno glacier (http://en.wikipedia.org/wiki/Perito_Moreno_Glacier) and that if you can afford it you stay at a place called Los Notros. (http://www.losnotros.com) (warning: there is sound once the file loads, so don't look at work... )

Patagonia is actually not a state, it's an area that covers both Argentina and Chile (like "the Amazon" or "the Alps"). There are a couple of natural/easy crossing points between the 2 countries, and knowing these will make your trip much easier. Bariloche is not in Patagonia, it is in the Lakes District. It is one of the main crossing points between Argentina and Chile.

This is an amazing area of the world and if you like nature, you will want to go back no matter how long you stay. I've done 2 trips to this area of the world and would be happy to share my thoughts/hints. PM me with your phone number and I can give you a call -- I'm on the west coast of the US (in spite of my FT handle).