Well considering how much I run on, I guess I should hope so
And I'll give you the short answer first this time: "no" and "yes," respectively.
No, I know of no tradition, rabbinic or otherwise, within Judaism of expecting the Messiah to
be God, and in fact this was acknowledged as early as the early 2nd century by the Christian writers Justin Martyr and Saint Hippolytus (i.e., that the Jews didn't profess this--obviously they did). "Come from," on the other hand--I'm not sure what that phrase entails to you, but part of the reason why I mentioned the various midrashic traditions of an "eternal Messiah" was to highlight that there clearly were some more mystical notions (or perhaps I should say, "were/are"--I'd describe some of the Hasidic notions as quite mystical, certainly) floating around, all of them drawn from midrashim (oral lore, of which there are abundant collections, many of which make cameos in the Talmud). The most common ones seem to have been those I cited above: that the Messiah was created even before the world was made; that he exists in some sort of potential form in every generation (which in turn entails the idea that a person with Messianic potential won't fulfill it unless Jews collectively do their part to uphold the covenant); and that he'll actually be a reincarnation of David, not just his descendant. Occasionally the title
bar enosh--"son of man," normally used in Biblical Hebrew in the more general sense of "mankind," or to refer to a high-ranking angel, but in these cases clearly taking on a more specific meaning--is attached to the Messiah in such midrashim. In midrashim only, there's also an alternative tradition where the Messiah gets bifurcated into two distinct people: a "Messiah ben Joseph," who undertakes the military aspects of the job but ultimately fails (this has him fighting either Persia or Rome, depending on which midrash you're reading), and a "Messiah ben David," who resurrects ben Joseph, thus enabling him to finish off the gory bits, while ben David busies himself with the more spiritual aspects. This midrash is sometimes explained as a folkloric attempt to reconcile two contrasting scriptural images of the Messiah: the triumphant military conqueror and crusher of foes on the one hand, and the humble humanitarian who rides into town on a donkey on the other.
So yes, for a self-professed Messiah to also equate himself with God would certainly have been "extra shocking," though of all the titles (publically) ascribed to Jesus in the Gospels, only "Son of God" strikes me personally as likely to have been unambiguously taken by an average Jew as "he said he's God." The Gospel passages in which this title is linked to
gidduf, "blasphemy," in the sense of a capital crime, have always puzzled me somewhat. The definition of
gidduf in Mishnah (Jewish law, which in its current, "Pharisaic" form became the law of the land in 75 BC--though it's unlikely the previous form was much different) derives from Leviticus 24:10-13, and specifically means invoking God's name in a profane context (as opposed to the 3rd Commandment,
lo tissa et shem ha-Shem Eloheicha lashav--not doing evil in God's name--or
apikorsos, heresy, a noncapital crime with the general connotation of professing false doctrines). According to Mishnah,
gidduf, whose pronouncement required all within earshot to rend their clothes--as the Sadducee Caiaphas does during Jesus' trial, confirming which crime he's accusing him of--was punishable by death (through stoning only, crucifixion not being a Jewish form of punishment) solely when the Tetragrammaton was invoked: profaning ha-Shem, Elohim, etc. warranted a flogging instead. The maximum punishment of stoning, which like all capital punishments first required a trial before a court of at least 23 and the presence of at least two witnesses (or else it was murder, and itself punishable by death), was carried out in this manner: the first witness threw the convicted party from a height, then if that did not prove fatal the second witness dropped a large stone on their head, then if that still was not fatal, an assembled crowd of all who heard the blasphemy finished off the job with a hail of smaller stones. That such a punishment would ever have been spontaneously meted out
sans trial by rock-chucking mobs, as suggested by the Gospel of John, is hard to believe, and it's harder still to believe this could have occurred in Roman times, when capital-case jurisdiction was reserved for the Roman authorities (per Josephus and, for that matter, John himself; interestingly, Josephus' account of the trial and stoning of St. James attributes the Sadducees' action there to an authority vacuum brought about because the procurate, Festsus, had died, while the new one, Albinus, had not yet arrived). As far as the Sanhedrin trial, only in Mark's and Luke's accounts does it seem to be the case that Jesus might have pronounced the Tetragrammaton (assuming the Greek--
ego eimi--here stands for that, as opposed to mere affirmation, which it can also convey). If so, this might plausibly constitute
gidduf--assuming that Caiaphas' question used "Son of God" to denote divinity, as opposed to Messiah-ship (as David is also called this in Tanakh). At any rate, since the Sanhedrin didn't have capital-case jurisdiction and the Romans didn't consider
gidduf a capital crime, I never really understood what the point of this whole exercise was supposed to be; the trumped-up accusations which Luke has them relaying to Pilate--inciting revolt ("through-turning our nation"), opposing payment of tribute to Caesar, and proclaiming himself a king--seem perfectly sufficient for their purposes, and indeed it's only the latter charge that Pilate seems to take even the slightest interest in (presumably because it could, in theory, warrant crucifixion under Roman law--a verdict both Tacitus and Josephus attribute explicitly to Pilate).
[* Many historians speculate that the Sanhedrin, and particularly its Sadducees, had been especially irked by Jesus' disruption of Temple vendors, which seems plausible; however, Jesus was hardly the only rabbi to ever take offense at this, as the Talmud records several complaints by diaspora rabbis of having to clamp down on the same behavior, and encountering stiff resistance for it.] Plus, if it was really all going to wind up being decided by fiat by some random mob who apparently couldn't articulate any motive beyond bloodthirst, again, why bother?
Nonetheless, as late as the era when the Talmud was written down (ca. 200 AD in the case of the written Mishnah, which is the layer in which these references appear), Christians living within the Jewish community were still considered
minim, literally "creeds," a word denoting some 24 different sects (Gnostics, Samaritans, Sadducees, etc.) which were considered heterodox sects of (rabbinic) Judaism, not wholly different religions. Although it's seldom specified which
minim were meant in the various passages using this word (and many of the passages don't seem to intend specifity), it can sometimes be reasonably deduced from context which sect was meant; for example, Christians were almost certainly among those "covered" by the doctrine of
shidduf, "association," a ruling that for
minim to worship God in corporeal form is not heresy if "their intent is on the Master of Heaven and Earth, for then they are only associating something with God." Passages clearly dating from after the Great Zealot Revolt (70 AD) suggest a distinct souring of relations with
minim generally compared to earlier passages, which is not surprising, as that would indeed likely have been a polarizing event. From then on, there are increasingly hostile accusations of converts to
minim becoming informers for the Romans etc., and the incidence of apparently friendly debates on points of law, interpetations of scripture, etc., drops off considerably. Of course many of these passages can't be dated definitively at all, but at any rate, according to St. Epiphanius who was a Judaean monk at the time, by 336 the situation was bad enough that Constantine had to issue two joint decrees: one barring Jews from assaulting Jewish converts to Christianity, another barring said converts from burning synagogues and violently disrupting Jewish worship services. (Christianity by this time was fully legal, but not yet the Empire's official religion; Judaism was legal, although conversion to it was forbidden.) And in 325, the Council of Nicaea, in ruling to finally uncouple Easter from Passover, had determined that (quoting Bishop Theodoret of Cyrrhus) "
t was, in the first place, declared improper to follow the custom of the Jews in the celebration of this holy festival, because, their hands having been stained with crime, the minds of these wretched men are necessarily blinded...Let us, then, have nothing in common with the Jews, who are our adversaries...avoiding all contact with that evil way...Therefore, this irregularity must be corrected, in order that we may no more have any thing in common with those parricides and the murderers of our Lord."
So, at what point a mutual self-understanding as two wholly distinct religions emerged is difficult, if not impossible, to date precisely; but unfortunately, whenever it did, it failed to bring about longterm peaceful coexistence.