7 Days In Brazil

Where in the US are you flying out of? The trick to doing this trip is to coordinate flights while not exhausting yourself and still seeing a few sights.
Flights to Brazil are often overnight, pretty arduous in coach even from a 'close' airport like Miami, and more so if you have to make connections before leaving the US. You are probably better leaving Wednesday. That probably gets you into São Paulo (or Rio)at dawn on Thursday, half asleep and barely functional. It will probably take over an hour, up to two, to get through passport control, pick up your baggage, and take it through X-ray and customs.
If you are still game, you wait around for another flight to the falls. Both Brazil and Argentina have airports at the falls. Most flights from Brazil are cheaper if you fly into IGU in Foz do Iguacu iirc.
I would suggest stopping at the falls on Thursday night and doing some sightseeing on whatever side you end up on. There are things to do on both the Brazilian side of the park and the Argentine side, and the views are very different. Some people like staying in Foz and some prefer Puerto. Maybe cross the border by local bus and stay in Puerto to see some of the Argentine side of the park. I never rented a car while there, so I don't know if there is any advantage to renting one at IGU for going into Argentina, or renting on the Argentine side. You will be signing a contract that you probably can't read anyway. Personally, I'd just make my way across the border to Puerto Iguazu, maybe do a bit of sightseeing in the park there, and find a bus to Posadas on Friday. Or drive the 3-4 hours, with time to see the countryside. You might have time to see the mission on arrival.
Saturday is the wedding you came for.
Sunday drive or bus back to the falls, see what you didn't have time to before on the Brazil side, and get a late flight ( there's a 6 pm direct from IGU to a Rio GIG) to your exit city. I'd pick Rio to fly in/out of. I lots to do and see there for Monday and Tuesday. Tuesday late night flight back to the US, arriving on Wednesday morning, mid day with connections.

The normal thing for tourists is to spend 2 days seeing Iguassu, for the Argentinean side as well as the Brazilian side. But in your case, I think you could see the Argentinian side of the falls on your way back from the wedding, if you leave early enough in the morning.

If you can visit the Brasilian Side the afternoon you get back (it only takes an hour or two) then it wouldnt be too bad.

Though, I would be inclined to ditch Sao Paulo and go straight to Rio. Sao Paulo is fine but Rio is so much better for the tourist/traveller.

I've been to Foz do Iguazu and the falls several times and I'd say one day there is enough (I haven't been to the Argentinian side of the falls though). In the city, Puerto Iguazu, there's not much to do, tiny town with some commerce, you can buy slightly cheaper wine and try a restaurant but nothing more than that. The same with Foz do Iguacu in the brazilian side.

I agree with trent on skipping Sao Paulo unless you like huge cities with lots of shoppings, large distances and not much sightseeing to do. Spending more days in Rio is definitely worth it (like 5 days). I wouldn't do more than that with the amount of days you have.

Enjoy! =)

Thanks for the advice!
@maracatu: we are flying out of Chicago, so we will definitely have a layover in the U.S. Unfortunately we are unable to take any extra days off with work, so we are locked in to flying out Thursday late afternoon/evening which puts us in South America on Friday.

Does anyone know how much a bus ticket is from Iguazu directly to Posadas? I tried searching online but was unable to find if tickets are available for advance purchase, or if we have to buy them the day of at the station.

From the sound of it, we may just skip Sao Paulo and fly directly to Rio and spend more time there. It looks beautiful!

Well, maybe you have a magic carpet (or a magic travel agent), but say you take a Thursday 4:25 flight out of Chicago (AA), with a stop in Miami, you get into a Rio at 8:30 am, Friday, which does not give you time to get through immigration, get your bags, get through customs and still make the check in for either the GOL direct (2hrs) flight to Foz or the TAM one, both at 10ish in the morning. So you wait for the next flight that makes one stop, takes 6-10 hours, and arrives at best just before 6pm.
It would not be advisable (or probably safe) to cross the border, rent a car (or rent and then cross) and drive 4 hours in the dark in a, no two, strange countries.

I see online that the Aristobule del Vale bus company goes from Puerto Iguazu to Posadas.

Good luck.

Maybe you can research going through Buenos Aires to Puerto Iguazu, and on to Posadas. Perhaps there are better BsAs to Puerto Iguazu connections.