The mainstream view is that he probably did not claim to be God as that would have been anathema to Jewish theology. I think there is a general consensus that he claimed to be the Messiah, but that was not the same as a claim to personal Godhood. The Jewish Messiah was not God. The mainstream consensus, basically, is that Jesus moves from a "lower Christology" to a "higher Christology" over time.

My impression of the scholarly consensus was that the historical Jesus was an apocalyptic prophet who preached similar ideas to that of other apocalyptic prophets of the time (like John the Baptist), namely that the kingdom of God was going to arrive on earth soon -- as in, in his lifetime -- and that one should reconcile themself to God immediately. It seems that many of his followers believed this as well. Similar apocalyptic visions can be seen in other books such as Daniel.

I'm basing this mostly on Bart Ehrman's book "The New Testament." I realize he is a controversial author with his later books, but that book in particular seems to do a good job of citing and summing up the historiography on the subject, and is often used as a textbook for that very reason.

I don't recall a consensus on the fact that the historical Jesus claimed to be the messiah, if anyone can list any sources that indicate that, I'd appreciate it.

The most important thing to remember is that monotheism was a very complex theological development in the Persio-Hellenistic era towards late antiquity. An important movement during this period was known as binitarianism and this is probably the religious framework from which Christianity originates. Within this form of Judaism, it is understood that there is a plurality within the divine, between the Memra (Word) of God and God. The only thing that really makes Christianity distinctive is not its theology but rather that the Word of God is understood to have been personified in Jesus; otherwise just about everything else that the earliest Christians believed was at home within the second temple era. What this means is that it was not altogether heretical for any Jewish people who understood themselves to have been the Messiah to have professed a form of divine status; 11QMelchizedek actually paints the picture of a divine priest-king, probably someone who was actually alive and known by the Qumran communities. This is why I'm not averse to an early high Christology, it wouldn't surprise me if much of it goes all the way back to the thoughts of Jesus himself. It makes me a tad bored when contemporary scholars attempt to present an historical Jesus who is so thoroughly rational and has no mythical dimension.