I found a website that has gone to some lengths to challenge the accuracy of this assertion, claiming that the subject of the statement (Jesus of Nazareth) was not really a carpenter. Fair enough.
What caught my attention (more than the "Was He a carpenter or a Rabbi?" question) was the assertion that Christ our Savior was Jewish. The term "Jew" (and the various original pronunciations of it) apparently emerged during the Babylonian captivity (those 70 years [597 to 515 B.C.] during which the southern Palestine tribe of Judah [plus some of Simeon, Levi and Benjamin] mixed with the Babylonians [before eventually repatriating to Judea]).
So, from 515 B.C., the (Judahite) people of the captivity were back in Jerusalem, now being nicknamed "Jews". Earlier, back in 722 B.C., Shalmaneser and Sargon II had rounded up the people (Israelites) of Ephraim/Samaria for deportation northward into Assyria (the effective disappearance of the "10 tribes"). Not all were deported. Some of the "10-tribed" Israelites made their way south to Jerusalem.
In 157 B.C., John Hyrcanus, the leader of the Edomites (Idumeans) from Mt. Seir, invaded Judea, and the two peoples were intermingled and perhaps permanently fused. The Edomites brought with them many of the teachings and traditions of the Talmud. Clearly, by the time of Jesus's appearance in Jerusalem a century and a half later, southern Palestine/Judea was a melting pot. Edomites, Jews, Edomite-Jews, Romans, and Israelites lived in close proximity, and did not always get along. After Jesus leveled some pretty searing indictments at the Jews (and they at Him), they crucified him.
So the crux of the question is - did Jesus descend from the same Jewish population which murdered him? As a resident of Jerusalem in Judea, Jesus was, by residence/nationality, a Judean (despite his family having come from Cornwall, England). By lineage, however, was He a "JEW" or "Jewish"? For the answer I decided to do a quick Google search and turned up the following webpage - which I found enlightening.