It's probably safe to assume the populations of the old world is roughly analogous to what they were in the 14th century or so. And we know that US/ and Canada is roughly 61 million. So how many people live to in the nations to the south?
The first instinct would be to reduce the population by eighty percent, which would result in a combined populaton of 117 million. (Or 104 million if you were to draw from 2003 populations, when the blog was original written.) But a question I asked myself--much of this are was settled and colonized for centuries before Anglo-America, but it tended to be less populated until the 1950's, that is, heavy industrialization. Considering Florida, one of the most populated states in Industrial America and the most tropical region in the continental U.S., took a major population crash, would that apply to Mexico, Central and South America?
I decided to take a two-prong approach. The first was de-urbanization. I multiplied the population by the percentage of people who did not live in big cities. It's a pretty handy trick--the U.S. is about 80% urbanized, which is also the number by which Medieval America is reduced. It's not a perfect system. De-urbanizing France gives you numbers it would be at in the Middle Ages, but applying that to Great Britain gives you 12 million--more than the island can actually contain. So part two involved looking at the populations for these countries from about 1885-1890, as that would be the period the U.S. had a population a population of 57 million. This is also imperfect, since the U.S.'s population at the turn of the century was a discordant mix of burgeoning industry and an unsettled west, but that in so many cases, a late 1800s population was also its de-urbanized number means I'm probably onto something. Anyways, I added the two figures and averaged them. Making me more confident still was that I found the population of western South America matched that of the Inca Empire at its height.
The population would be about 66 million or so. About half of them inhabit the the are known as the Spanish main, the oldest settlements of the New World, probably a well-traveled part. As mentioned on the trade page, the Gulf Mexico is an important trade gateway, making the coasts very busy. For the most part, the denizens aren't too far removed from the coasts, and they wouldn't be given much incentive to start now. Central America pretty narrow, Except for ancient tribes, the interior of South America is pretty spacious.
An outlier for this would be South America's "Southern Cone". I actually upped Brazil's population from the average, giving it a still precipitous dip of 20 million to its modern 200+ million. This is because the lower area around the Parana (where it also borders other countries like Argentina, Uruguay) is relatively temperate, very fertile, making it a solid counterpart to Ohio, or Medieval France. The only thing that might keep the population from exploding too much is the possibility of wars breaking out over this very busy intersection.