President Obama is making a one-day stopover in Copenhagen to lend his support to Chicago's bid to host the Summer Olympics in 2016. Chicago is one of four finalists, along with Rio de Janeiro, Madrid, and Tokyo. Rio and Madrid were said to be the early leaders in the highly-politicized, somewhat parochial voting by the International Olympic Committee, but Chicago's star has risen at the expense of Madrid's, and now it is thought that it may be close between Rio and Chicago.
Rio's bid is extremely ambitious, costing an estimated $14 billion (Tokyo's would no doubt be the cheapest, as it hosted the Olympics in 1964, but that fact--that they hosted fairly recently--would count against it). Brazilian President Lula da Silva is also in Copenhagen and is making a strong plea for the first Olympic games in South America (in terms of Third World countries Seoul, S. Korea, which hosted in '88, might have an argument, though somewhat weaker than 2008's Beijing).
Brazil is doing well these years and has the right to bid for an international coming-out party such as Beijing's. I would suggest that the fact that Chicago's bid is for an estimated cost of "only" $4 billion would make it a better candidate, one with less risk for choice. Obama's strong international popularity will work for Chi-town's case, and apparently the swing group will be the African states (let's say he might help with those, too).
What the condition of the US economy will be in 2016, and whether it will need the boost Olympics bring (and preparation for it, as well) is anyone's guess.
Perhaps Brazil could win a vote now for 2020, which would give it more time to successfully complete what would be a huge effort to prepare the city. A better comparison that Beijing might be Athens' Olympics of 2004, which was a difficult prep.
I have been to Rio a couple of times--it is one of the most beautiful cities in the world, so it would be a spectacular site for the Olympics. The fact that it would be winter during the normal time of the summer Olympics is not actually a problem--it would be temperate then, whereas it would be intolerably hot in their summer (December-February). Rio is a city that is much larger than most people realize, and it has enormous, widespread favelas (slums) which will need to be isolated from the Olympic competitors' experience (if not their sight--mostly they're on the huge, steep hills found throughout the city). That--making the city safe from criminal influences coming from the favelas--would be just one of the major challenges; transportation (they have enormous traffic jams, and little public transport) would be another. I think it's worth it, but they could use the extra four years.