In the Discovery Channel show Ice Age Columbus, researchers in Canada found that 25% of the Indians there had some European blood, which solidifies the European theory.
There has been continuous European contact with the Indians of Eastern Canada (Ontario, Quebec, and the Maritimes) for at least 400 years. (The same holds true for the Indians of the U.S. Eastern Seaboard.) Moreover, the contact has primarily been with Western Europeans, mostly French and British. The modern day French and British have some genetic similarities with the Ice Age inhabitants of Western Europe, a few of whom are supposed to have arrived in eastern North America. How can Western European genes from 10,000 years ago be distinguished from those of modern times?
Sorry, that theory is an old one which has been shot down by recent scientific studies.
The X gene found in a few Western Native American tribes is X2, which is Asian in origin, in particular, the Altaic region of Siberia.
The X gene found in Europeans is X1.
Both X1 and X2 are derived from people who originated in the region of Northern Iran.
The X1 went west, the X2 went east.
The genes don't lie.
This is what the Altay look like, which is exactly like Native Americans: