Unfortunately, this is the kind of debate where we have no reliable, unbiased, nonpartisan sources. How could we?
We are forced to fall back on the “But that’s too stupid for words!” method. While a fair chunk of the canonical Bible fails the test I’m seeing that far more of the non-canonical books do. The Gospel of Thomas? At least Zen koans can make some sense if you think about them but some of those sayings are internally contradictory (hard to do in forty words) besides being diametrically opposite of everything else Jesus was supposed to have said. They are dope-slappingly stooopid and, therefore, quickly discounted. Then there’s the Gnostic crap, which tends to the “crazy as a shithouse rat”/Scientology end of the theological spectrum so we toss it. Finally, we have what Celsus and the Talmud say, which combines the feasible (Mary was raped or had an affair with a Roman soldier with a name almost as stupid as Biggus Dickus) with the nutsy-cuckoo Egyptian Mojo shit. While I’m not married to the Divine Jesus thing this story seems obviously and intentionally insulting.
Tapping my foot impatiently and checking my watch, waiting for Diogenes and his lantern to show up.
Given the Virgin Birth thing the bloodline of Joseph is irrelevant surely? 
Well, you or I might say that. Maybe Joe adopted Him, but wouldn’t “This is my beloved Son, in whom I am well pleased,” then trigger a big custody battle?
“Sorry, God, but when You signed the adoption papers You relinquished Your parental rights.”
God strikes Joseph down with a lightning bolt. “Relinquish THIS, asshole!”
Bet you always wondered what happened to Joseph. 
The actual ANSWER to the OP’s question is that it’s impossible to know now and it was impossible to know THEN. There are – and were – no reliable extant records for descendants of David into the Herodian era. Matthew and Luke both created (independently of each other) fictional genealogies for Joseph but those genealogies are contradictory and clearly fabricated (one of them goes all the way back to Adam) and Joseph’s bloodline could not have been traced very far in any case since he was unimportant member of an illiterate sub-peasant class who wasn’t even from Judea. Nobody was bothering to keep family records for hick laborors from the sticks of Galilee. Aside from that, both Matt and Luke denied that Joseph was Jesus’ real father anyway, so Joseph’s bloodline is irrelevant in any case. Under Jewish law the royal bloodline could not be passed through either the mother or through adoption and under Jewish religious and Biblical expectations, the Messiah (i.e. the heir to the throne of David) HAD to be a direct blood descendant of David through his father.
The apologist meme that Luke gives a genealogy for Mary is hogwash, by the way. Luke’s Gospel clearly states that he’s giving the bloodline for Joseph, he doesn’t even mention mary’s name, and the Mother’s bloodline was irrelevant in any case.
To summarize, it’s entirely possible that Jesus (or any other random person off the streets in the Herodian Kingdom) was descended from David (if he existed), but there was no longer any way – even then – to know it or prove it.
I do think it’s interesting, though, that under Jewish law, anyone born of a virgin is automatically disqualified for any claim to Messiahship. I think that most Christians aren’t aware of that.
Cite for that last statement? Not that I doubt you. It just sounds funny.
And how about the Joe as laborer vs Joe as contractor thing?
The Messiah, by definition, is the heir to the throne of David. Under Jewish law, that throne can only be inherited by direct patrilenal descent from David. No father = no inheritance.
Here is a list of the Jewish requirements for the Messiah from Jews For Judaism. The third item on the list states the requirement that he must be a direct descendant of David.
Nice try on Tabor’s part, but unlikely. Tekton literally means “builder” in Greek and it referred to a variety of grunt laborors, including carpenters, bricklayers and stone masons.
John Crossan (my source for what I know about this class), says that tektons (or as he calls it, “the artisan class”) was a bare subsistence class below even that of peasants. It may be that Tabor is aware of a usage of the word to include contractors but it’s not a use I’ve ever heard of before and everything I ever have read says that tektons were dirt poor piece laborors, worse off even than farmers.
But the Gospels portray Jesus as having a rabbi’s depth of knowledge about the Scriptures. If he grew up that poor, how did he come by his education?
He couldn’t have. An estimated 95-98% of the Palestinian state was illiterate in the 1st Century (I’m citing Crossan again here). It’s highly unlikely that Jesus could read or had any formal education at all. I’ve seen some comjecture that Jesus could have learned to read when he was being trained as an Essene, but I think that’s pretty wild speculation.
Having said that, he could conceivably have been a scriptural prodigy without being literate. It’s not unusual for non-literate people to develop extraordinary facilities with verbal memory and mnemonic devices for recalling extensive amounts of orally learned text. A bright kid who spent a lot of time in the synagogue could probably pick up a lot of scriptural knowledge and be able to cite passages from memory. It might not have even been all that unusual. What might make a kid “prodigious” would be an ability to summon up scriptural arguments in a clever (especially if it included an appropos quotation from the Torah or from a prophet) way to defeat a few blowhards in the verbal jousting that was common in synagogues as well as the Temple.
I suppose that, to draw an analogy, it might be comparable to a very bright kid who watches a lot of Court TV and learns enough trial procedure to be able make a clever argument in a legal debate with a real lawyer or cite a surprisingly on point precedent from memory. A REALLY precocious kid might really be able to impress somebody.
In the case of Jesus at the Temple (or any of the exchanges with Pharisees) we have an apocryphal story which is not meant to convey that Jesus had formal training but just the opposite- that this hick kid from Galilee was able to defeat those fancy, pompous scholars from Jerusalem.
Didn’t the Jewish boys have to learn to read at least enough Hebrew to read out a verse at their bar mitzvah? Or did that custom emerge later?
Bar Mitzvah ceremonies, as such (and the tradition of the call to Torah), only arose in the Middle Ages. In ancient times, a child reaching the age of majority was marked only by a blessing from the father.
As I mentioned in another thread, King David was a polygamist and the Bible names at least 18 sons he sired. Even if you discount all of them but Solomon, Solomon’s son Rehoboam, who was King of Israel, had 28 sons (and 60 daughters), and this was at least 7 centuries before Jesus. Thomas Jefferson died and has thousands of living descendants by his wife alone in spite of the fact only two of his daughters survived to adulthood and one of them had only one child (and if you add in Sally Hemings’ descendants the number probably more than doubles to more than 10,000 living descendants, so a polygamist like David or Rehoboam would have descendants all over Israel and it’s not inconceivable that Rehoboam could have been a direct ancestor of every male of Jewish ancestry in Israel by that time, therefore there’s no reason to suppose that even if one or the other genealogy was true and known Jesus would have had a claim to the throne (besides which Jesus had no known children and several brothers who would have inherited).
There is precedence for the throne passing through a daughter’s line in the Old Testament. Athaliah, the daughter of Ahab and Jezebel, came to the throne of Judah after her 70 brothers and half-brothers (and presumably their offspring) were put to death by Ahab’s enemies. Athaliah supposedly purged the kingdom of all David’s descendants, including her own son and grandchildren, but her grandson Jehoash was hidden from her and came to the thrown. Lot’s of problems with this story, beginning with the fact you’d have even by then (if the polygamous accounts are true) have needed an army of genealogists to wipe out all of David’s descendants, and the fact she was only queen in Judah and Israel was probably still chock-full of David’s descendants [and any Judean descendant would have probably run for the border]), but even presuming that the line had to be jumpstarted with Jehoash you’re still talking centuries of polygamous rulers.
Were the Maccabees/Hasmoneans descendants fo David? In any case, there’s a far more historically reliable record that Herod the Great cleaned house with them, including his two sons by Mariamne, a Hasmonean princess he married for political alliance (though he allowed his grandchildren, who included Herodias, the dancing Salome [one of many many in the family to have that name] and Herod Agrippa I to live]).
Speaking of the dancing Salome, Herod’s kingdom went to three of his surviving sons: Herod Antipas and his Herod Archelaus (full brothers by a Samaritan wife Herod took after executing Mariamne) and Philip (son of a daughter of a high priest). Archelaus caused a rebellion and was recalled by Rome, Philip died of natural causes, and the territories of Archelaus and Philip were divvied up with Rome ruling most of them through governors and procurators and Antipas ruling the rest. Antipas ruled Galilee, which did not (still doesn’t) include Jerusalem.
John the Baptist preached in Galilee and Herod had him arrested and killed as a gift for his niece/grandniece/stepdaughter (Herodians usually married their nieces and that makes for some odd family trees- that Salome married yet another uncle/great-uncle and had children who were the grandchildren, great-grandchildren, and great-great-grandchildren of Herod the Great). Since Galilee was his kingdom, he could do that.
Antipas had estates in Rome, Jerusalem, and probably other territories, but this is much the same as the King of Jordan having a home in NYC (which I don’t know if he does or not, just saying). The King of Jordan when he visits NYC is treated as a visiting head-of-state and with great decorum and respect, but he has no power within its borders. When Jesus was arrested Herod Antipas was visiting Jerusalem for the holy days, but he had no power- he was outside of the borders of Galilee.
HOWEVER, since Jesus was a citizen of Galilee (Nazareth was Galilean), and since Pilate was looking for an excuse to pass the buck anyway, he said “well, this guy’s from Galilee, he’s Herod’s subject- here ya go” and basically ‘extradited’ him, saying “Antipas, I give you authority to try your subject any way you see fit even though you’re in my territory. Antipas basically said ‘I’ll mess him up, but I know what you’re doin’ dude, I’m already up shit’s creek for the death of one popular Holy Man, not doing that again, SERVE!” and tossed him back after some rough housing.
Had Antipas demanded to try Jesus while in Jerusalem, Pilate could certainly have said no. (This is assuming the historicity of the Jesus’s trials of course- I’m not debating them.)