Interesting.
What is its know so far (verified and blessed by the academics) is that the first humans in the Americas are from Monte Verde, Chile, around 12.000 years BP. There is nothing so far that makes people suspect they reached South America thousand of years after crossing the Bering strait. It seems more pausible that the spread was quite fast.
On the other hand, it is known that species like the american lion and the fox spread all the way from North America to Patagonia. If those animals could do why humans couldn't do as well, and very fast. We know early humans were hunters and fishermen, and that lifestyle didn't force them to stay where they were born during a lifetime.