Here's the model from Wikipedia:
This hypothesises similarities between the Solutrean industry and the later Clovis culture / Clovis points of North America, and suggests that people with Solutrean tool technology crossed the Ice Age Atlantic by moving along the pack ice edge, using survival skills similar to that of modern Eskimo people. The migrants arrived in northeastern North America and served as the donor culture for what eventually developed into Clovis tool-making technology. Archaeologists Dennis Stanford and Bruce Bradley suggest that the Clovis point derived from the points of the Solutrean culture of southern France (19,000BP) through the Cactus Hill points of Virginia (16,000BP) to the Clovis point...This would mean that people would have had to move from the Bay of Biscay across the edge of the Atlantic ice sheet to North America. Supporters of this hypothesis believe it would have been feasible using traditional Eskimo techniques still in use today....
In my opinion there's all sorts of things crazy with this model. But genome blogger Diogenes has been harping on the possibility that a low level substratum component among Northern Europeans which has affinities to Siberians and Amerindians may be a remnant of the original European hunter-gatherers. It follows then that these groups were later marginalized and absorbed by waves of farmers coming from the Middle East and south-central Eurasia. David of Eurogenes Genetic Ancestry Project has discerned the same element, which is modal among Finns among Northern European groups. I don't think that the "Classic Solutrean hypothesis" is viable, where Paleolithic Europeans manage to jump across the polar fringe to North America.
Rather, my contention that it is not beyond the realm of possibility that a set of post-Gravettian societies spanned the northern fringe of Eurasia, and that one branch went east to populate North America.
Of those that remained it may be that on the milder fringes of western Eurasia, what became Europe, they were almost totally marginalized or absorbed. Only across the great expanse of Siberia where agriculture was marginalized did this people persist down the modern day. To bring it back to the present and over romanticizing the the possibilities one might then suggest that the displacement of Amerindians in North America over the past few centuries recapitulated the marginalization of their distant cousins in Europe between 5 and 10 thousand years ago! A major point I would like to enter into the record is that I believe that the single-demic-diffusion model is wrong for Europe. I now believe it is wrong for South Asia, where Austro-Asiatic speakers are I believe implicated in the introduction of rice agriculture to the northeast of the subcontinent. Unless programs like ADMIXTURE are saturating our pattern-matching cognitive biases a map of human variation tends to be difficult to reconcile with single population expansions in many areas (e.g., South Asia and Southeast Asia, and I believe Europe). We might not be able to make out the shape of reality very well because of the nature of palimpsest, but it is hard to reconcile the genetic variation with single-wave models. With the coming online of ancient DNA in northern Eurasia I think we'll get a better answer of what went down in the next 5 years.