Wow, old topic you found.
The Western Hemisphere was populated by millions; the population of Mexico was so large at the arrival of Cortez that the illnesses intro’d by the expedition spread rapidly; Bernal Diaz (the last, or one of the last survivors of Cortez’ band) noted that in “The Conquest of New Spain” — the large towns they’d marched through on the way to Tenochtitlan were full of dead and otherwise abandoned as they fled back to Veracruz. The population of Mexico didn’t reach those levels again until the 20th century.
That pattern of boom and bust in the population has been well documented via the chronology of the spread of urban centers, and appears to have followed the natural cycle of climate — the same kind of phenom that has been at work in Europe and the Med basin throughout history.
In North America, the drop of tribal populations was also due in large part to the introduction of diseases. Colonial period writers made note of abandoned tribal towns, in some cases actually giving the number of domiciles left behind. The population of North America east of the Mississippi was probably in the area of twenty millions at times, and had a similar boom and bust pattern. Similarly, the Mississippi basin and the Four Corners region of the SW had that boom and bust pattern.
The migrations that took place in North America seem to be related to climate change (though they have no fixed dates); here in Michigan the earlier groups were invaded from across Lake Michigan, about 1000 years ago; in the upper peninsula two unrelated groups fought something called the Rice Wars — the invading group having left Ontario and upstate NY.
20-200 million, huh. Probably 1 million people per square mile in Mexico City alone in 1491 and all their sewage was deposited on four tomato plants in the back yard. Yeah, I think I follow quite well the reasoning of those who like to pretend the history of yesteryear will follow their vain imagination.
Sorry, I still see no evidence to justify belief in more than maybe around 10000 in all of Mexico at the time of their arrival.