Hi there:
I am not very informed about this point, because genetic is not an important part in my education, what I know is that the Basque people have been going to nortk america for years an for sure, well before the rest of the europeans were able to make such a trip, it is known that when the first europeans met the Native Americans arround Newfounland, Canada and USA, these were greeting them saying "Apaizak Hobeto". This was a common phrase used by basque fishermen when they were asked this way. "Zer moduz?" (How are you) and the answer was "Apaizak hobeto".(the priests are better than me). So it does not sound impossible to me this genetic connection. You can find more about this in : www.albaola.com/index.php
Ikusi arte. (see u)

Dr. Steele of the Sioux nation has studied the Basque people as they relate to Native Americans. He says that the DNA of Basque and the tribes of the SE United States are very similar. He belives that the Basque may have been part of the people from this region.