Is it possible for a U.S. citizen to rent a car in Brazil? If so, what are the requirements, from the leasing companies, as well as the transit authority (to drive in Brazil)?
You need the drivers license from your home country an international drivers license that serves as a translation.
Even if there is no legal requirement for this (I found conflicting information on this), you cannot rely that the policeman who stops you in the road nor the clerk at the car rental knows English well enough to read your US license.
I am not Brazilian, and I successfully created a car rental reservation with Movida (http://www.movida.com.br/) to rent a car for 3 days during the World Cup. It was cheaper than going thru a service like Kayak or Priceline, etc. You pay in Brazilian Reales, it cost me about 220 BRL.
Brazilian company websites are kinda of mess in the UI/globalization area, but with a bit of help of google translate you can figure out all the fields and make a reservation.
The website forms often ask you for a CPF (Cadastro de Pessoas Fisicas - literally "Physical Persons Registry") which is like a SSN in the US. If you're a foreigner you can often leave it blank or there'll be check a box that says you're a foreigner. In the case that it still asks for something there, enter a passport number or something from your ID docs so they can pull it up.
Everything else is pretty similar to the US... you have to pay for insurance Loss Damage Waivers, etc, etc...
I am from Brazil and I will try to help you.
According to "Departamento Estadual de Trânsito de São Paulo" (Sao Paulo State Transit Department), here what they say about foreigner citizen driving in Brazil:
However, to drive in Brazil after 180 days, the foreigner must have the Brazilian license or a International license. This is based on reciprocity principle on Vienna Convention.
If you need more help about Brazil (and local laws), I can help.