Let's just say the facts get in the way of a good story. There's no connection between Native Americans and Jews, except in certain areas settled heavily by Anusim (Sephardic Jews who pretended to convert to Christianity, but secretly maintained Jewish traditions). For example, certain parts of the American Southwest, Mexico, Brazil and other areas -- but the DNA dates to the Anusim, who came with the Spanish, and then intermarried with Indian tribes (who were a lot friendlier to them then the Spanish). Not to far-fetched nonsense about "lost tribes" from the Assyrian conquest in 800 b.c.e., or the Roman conquest in 70 c.e.
This claim is particularly far-fetched: Josephus gives a pretty clear account of what happened at Masada. The few Jews who survived were taken as slaves by the Romans. They didn't escape, build a boat, and manage to beat Columbus by 1400 years (all while having little naval expertise).
If you want to look for "lost tribes," a much more credible candidate would be the Kurds. On the Y-chromosome, the Kurds are almost genetically identical to Jews. And they happen in inhabit the exact region that the Israelities were deported to by the Assyrians.