I have family who claim that their ancestor who was in Massachusetts by 1670 was from Russia, and was Jewish! What are the chances?
The possibility exists, and one particular family has claimed this heritage for over a century. Genealogical records are sometimes difficult to trace origins, but this is repeated on numerous genealogical sites:
"The name Lurvey is a good transliteration of the German, which is a common name among German Jews. There is a tradition in the Lurvey family that the first Lurvey who immigrated to Massachusetts in the 17th century [Peter Lurvey] was of Jewish descent, and came from Archangel in Russia."
Early publications, almost word for word, so probably some of the earlier records:
The Century Illustrated Monthly Magazine, Volume 59, in 1900.
John Gilley, Maine Farmer and Fisherman,By Charles William Eliot in 1899.
So this claim has been repeated in publications for over 100 years. Note the location, Archangel(Arkhangelsk), was a seaport and a center of trade at the time.
Concerning the number of Jews in Massachusetts, according to this article on the History of the Jews in Colonial America
The earliest mention of a Jew in Massachusetts bears the date May 3, 1649, and there are references to Jews among the inhabitants of Boston in 1695 and 1702; but they can be regarded only as stragglers, as no settlers made their homes in Massachusetts until the Revolutionary War drove the Jews from Newport.
From the text there it seems to state none were resident before the late 1700's. This doesn't discount the claim, however, as many immigrant ships arrived in Massachusetts, but the colonists would then move on to settle in other regions.
Concerning the presence of Jews in Russia,History of the Jews in Russia states
The presence of Jewish people in the European part of Russia can be traced to the 7th–14th centuries CE. In the 11th and 12th centuries, the Jewish population in Kiev, in present-day Ukraine, was restricted to a separate quarter. Evidence of the presence of Jewish people in Muscovite Russia is first documented in the chronicles of 1471.
but also discusses the fact that most major emigrations of Russian Jews took place later, so if Jewish individuals made it from Russia to Colonial America in 1670, they were not part of major settlement group or migration wave of similar individuals.
Again, however, an individual or family with the resources could certainly have made the journey.
The chances are minuscule: there were very little Jews in Russia in 17th century. Russia acquired major Jewish population only in the second half of 18th century with incorporation of Poland.
So those ancestors could be Jewish, from Europe, but I very doubt they were from Russia. Maybe from Eastern Europe, but hardly from Russia.