First, Jesus did not live in Judea, but in the more rural and distant province of Galilee. The major population center was Sepphoris, Herod Antipas' seat of power. Historians generally agree that Jesus would have plied his trade in that city:
Sepphoris... was moneyed. It was the center of trade for the area. And if Jesus were growing up in Nazareth, which is just a walk for somebody healthy... I think it's something like three miles. If he were a carpenter, or some kind of craftsman, he might have done work in Sepphoris....What does this imply about Jesus' social class? It's hard to know. I think that since he's depicted as a pious Jew, and since pious Jews have a six-day work week, and since on the seventh day they have particular obligations that don't allow them to take long journeys, (on the Sabbath you really are supposed to rest. You're not supposed to hike into Sepphoris and maybe, catch a play in the afternoon, or something like that.) I don't think that culturally, Sepphoris would have made all that much difference. I think as most people in his period who are not landed gentry, Jesus would have worked for a living for six days a week and rested on the Sabbath....—Paula Fredriksen, Boston University
The actual word used to describe Jesus and his father is τέκτων, which can descibe anyone from a worker to (meataphorically) an author. However, if we assume, as Dr. Fredriksen does, a Pareto distribution of wealth, it's extremely unlikely that either man was blessed with extensive leisure time.
Luke's account provides us with a number of clues to Jesus' economic situation:
He probably was related to a priestly family.
Jesus' parents offered "a pair of turtledoves, or two young pigeons.", which according to Jewish law, was a concession for someone who not afford a lamb and a bird as a purification sacrifice.
His family was free to travel to Jerusalem every year for the Passover Festival.
When Jesus left his family and his job to become an itinerant preacher, he was supported financially by some of his female followers:
Soon afterward he went on through cities and villages, proclaiming and bringing the good news of the kingdom of God. And the twelve were with him, and also some women who had been healed of evil spirits and infirmities: Mary, called Magdalene, from whom seven demons had gone out, and Joanna, the wife of Chuza, Herod's household manager, and Susanna, and many others, who provided for them out of their means.
The same women came prepare his body for burial in a borrowed tomb.
Recall that Luke, as a gentile writing for gentiles, would have had every reason to inflate Jesus' status (and therefore wealth) so it's striking that he is depicted as depending heavily on women.
As perhaps the most studied man in ancient history, Jesus represents a fascinating slice of life. While he was by no means rich, his family was able to afford a certain amount of leisure and he had well-to-do friends. We can be fairly certain that he did not suffer under extreme poverty, but neither was he self-sufficient.