They didn't come from the same crossers... there were different waves of widely separated migration from different Asian peoples and there is some reason to believe, based on similarity of tool types in eastern north America and Europe, that some early stone age Europeans may have arrived on this continent and blended in as well. There are some fairly strong physical differences and linguistic between American prehistoric groups of people as a result of having different ancestoral stock.
Supposedly, at least according to my grandmother, some of her Delaware Indian relatives had no white ancestry but did have relatively light complexion and blue or grey eyes. There are certainly large differences in the physical appearance of North American tribes, the Aztecas of Mexico, and natives of the Amazon River basin.