Without looking at text, I think Matthew says that everyone had to return to their place of origin - rather than their place of livelihood - to be taxed. That seems to me at least to present a huge logistical problem, and frankly, does not seem plausible at all.
No. They went to the place of their family name. Joseph was from the line of David so he took his family to the city of David, Bethlehem of Judea.
Quote from one article, dealing with the issue ...
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Luke went on to say that, “all were proceeding to register for the census, everyone to his own city.” (Luke 2:3) It has seemed a problem that the Jewish method of returning to one’s own tribal headquarters to be “numbered” was used for a census under Herod.14 The Romans usually took a census in one’s home town.15 However, in a census for inheritance taxation it would be expected that this would be conducted where the tribal records were kept, no matter who conducted the census. Joseph was a descendent of David of the tribe of Judah. David’s ancestral home was in Bethlehem, and in that town the land records and genealogies required for such a census would have been located. Or, simply, Joseph was born in Bethlehem but then lived in Nazareth. Joseph and Mary went to Bethlehem to register for this census, and there Jesus was born.
As will be seen in the following chapters, the evidence suggests a winter birth for Jesus. But, why would Joseph and Mary journey to Bethlehem in the middle of winter to register for the census? There are several possibilities. Joseph may have recently inherited some land. Since the special taxation was related to inheritances, Joseph journeyed to Bethlehem to claim his estate and settle any taxes due. He would have there registered his property for the census. Or, perhaps Joseph had recently become eighteen years of age, and as an adult was required to then register as an independent household.16 Or, they had recently married, and the registration of the family was required. Or, Joseph and Mary thought that their child might be the promised Messiah and that the Messiah was to be born in Bethlehem (Mic. 5:2). They may have timed their trip to Bethlehem for the census to ensure that Jesus was born there. Also, registration may have been required before the end of the Roman year, that is, December 31, and they were late. However, there is no need to require that Joseph’s registration occurred immediately after the census for taxation was decreed. There are other possibilities, but these are mostly speculation.
IV. Conclusion
In support of Luke’s description of the census that brought Joseph and Mary to Bethlehem, it is confirmed that Augustus did decree a 5% world wide inheritance tax to support the military. This was sometime before the second taxing in 6 CE and likely before Herod’s death in 4 BCE; it was at some point discontinued. When this census took place cannot yet be determined, and Quirinius’ official status at that time is unknown.
An alternate translation suggests that Luke was actually saying that the census was only the one before that when Quirinius was governor of Syria in 6 CE. Luke was not saying he was governor when the first census was taken.
It does not seem presently possible to establish an earliest limit for the birth of Jesus. As such the search must go elsewhere to establish the date of His birth. As will discussed in the following chapters, the conception of John the Baptist and Jesus offers a surprising answer.
http://www3.telus.net/trbrooks/firstcensus.htm
The Jews of Galilee went to Jerusalem on the principal feasts, such as Passover. But I think people have not looked at the nativity accounts in Matthew and Luke. Matthew does not tell us in Chapter I where the annunciation took place. But Chapter 2 begins by telling us that Jesus was born in Bethlehem, and then we go to the story of the Wise men, the massacre of the innocents, the escape into Egypt, and the return not to Judea, but to the North. Luke tells a different but not contradictory story. He begins in Nazareth, then tells the story of the Baptist and Mary’s visit, before shifting back to Nazareth. We then tell of the journey to Bethlehem and the familiar events surrounding the birth. then of the circumcision and the presentation in the Temple. Then the rerun to Nazareth? Why the differences? The two men had heard different facts and had stitched together stories to fit the facts they knew. But we don’t know the time-lines they had in mind.