According to the Center for the Study of the First Americans web site:
In the Last Glacial Maximum, at the time of the middle Solutrean period, a permanent ice rim connected the southwest coast of Ireland to the Grand Banks. In winter, the Atlantic froze as far south as the Bay of Biscay. The Gulf Current that today extends across the North Atlantic was shifted southward; it circulated clockwise, moving toward the Grand Banks and returned to the Bay of Biscay. Contrary to popular belief, the North Atlantic at this time was not unremittingly hostile. Short-term intervals and possibly longer periods of moderate weather would have enabled even inexperienced navigators to sail along the ice rim. Eventually hardy sailors would have traveled the short winter route to the Grand Banks, stupendously rich in fish and game. From there the leap to North America was assured.
I'm convinced they came. I just don't know which way.
Bye, Bye Beringia (8,000 Year Old Site In Florida)
The DNA from these folks have been declared to be 'European.'