Is it likely and/or possible that Vikings interbred with Native Americans?

We only have to two records for Norse interactions with native Americans: The Saga of Eric the Red (Eiríks saga rauða) and the Saga of the Greenlanders (Grænlendinga saga). These describe trading and physical conflict with the Native Americans, and both refer to short-term visits. Obviously we should be wary on over-reliance on the use of sagas, but it does give us a good idea of what Leifr Eiríksson and Þorfinnr Karlsefni parties encountered.

Regarding L'Anse aux Meadows, we honestly cannot know how much intermingling went on between the Norse and the Natives. The archaeology finds have been fascinating, but it doesn't tell us much about the relationship between the two groups, beyond the trade. L'Anse aux Meadows is thought to have been abandoned within 80 years of its establishment, just as the settlements in the sagas were quickly abandoned. We can only begin to guess regarding inter-breeding, but considering separate language, culture, a past of conflict and a fairly small Norse settlement group, I'd personally posit that it was very unlikely and probably never occurred.

So essentially, yes it was in theory possible that the Norse and Native Americans could have interbred, but it's likely that it did not happen, or if it did, it was limited to one or two extraordinary circumstances.

However, recently teams identified possible Norse settlement sites on Baffin Island and the Avayalik Islands, if these turn out to be legitimate sites, they could drastically change our understanding on Norse settlements in the New World.

Source on Vinland: Wallace, B. 'The Discovery of Vinland'. in Brink, S. and Price, N. eds. The Viking World (New York: Routledge) 2008 pp. 604-612

Sources for the discovery of possible settlements: http://ngm.nationalgeographic.com/2012/11/vikings-and-indians/pringle-text http://news.nationalgeographic.com/news/2012/10/121019-viking-outpost-second-new-canada-science-sutherland/