So no one could possibly have made it across the Bering Strait because the water wasn't frozen; therefore the likely scenario is that people came to the Americas from Europe, across the Atlantic in boats. Sounds like good, solid logic to me.
I suspect that people came from just about everywhere to America. Maybe some came acoss that land bridge. It is looking more and more likely that people came to the west coast in boats, too. European origin seems prety certain for some contribution.
I think there is strong evidence supporting the theory that people did come over the Bering Strait, but evidence emerging that people also came to America from Europe and the Pacific Islands. Indians probably came from several places.