Argument 1: Was Quirinius "Ruling" in the Region?"Historical sources indicate that Quirinius was favored by Augustus, and was in active service of the emperor in the vicinity of Syria previous to and during the time period that Jesus was born. It is reasonable to conclude that Quirinius could have been appointed by Caesar to instigate a census-enrollment during that time frame, and his competent execution of such could have earned for him a repeat appointment for the A.D. 6/7 census (see Archer, 1982, p. 366). Notice also that Luke did not use the term legatus—the normal title for a Roman governor. He used the participial form of hegemon that was used for a Propraetor (senatorial governor), or Procurator (like Pontius Pilate), or Quaestor (imperial commissioner) [McGarvey and Pendleton, n.d., p. 28]. After providing a thorough summary of the historical and archaeological data pertaining to this question, Finnegan concluded: “Thus the situation presupposed in Luke 2:3 seems entirely plausible” (1959, 2:261).
Finegan, Jack (1959), Light From the Ancient Past (Princeton, NJ: Princeton University Press).
Argument 2: Historical Evidence for Quirinius and the CensusAnd as for Quirinius being the governor of Syria during this census, it is worth noting that the Bible never calls him the governor, at least the New King James Version doesn't. It says he was governing in Syria. And we know that Quirinius was indeed governing in some capacity in this region at this time.
Records also indicate that Quirinius was no minor figure in Roman politics. His name is mentioned in Res Gestae - The Deeds of Augustus by Augustus placing him as consul as early as 12 B.C.
After Caesar's young son Caius was sent to administer Syria as an Imperial Legate in 1 B.C., the Roman historian Tacitus mentions that Quirinius was then sent by Augustus to be an advisor to Caius while in Armenia around 1 A.D.
Evidently, Augustus wanted someone who was experienced in previously administering the region to advise his son. Who better then Quirinius?
The Biblical census was probably implemented by Herod at the command of Rome to coincide with their decree that all peoples should take an oath of allegiance to Augustus which took place in history around 2 B.C.
This oath, forced upon everyone in Israel, is recorded by the first century historian Josephus.
Josephus also mentions that Quirinius became governor of Syria, many years later, after Herod the Greats son, Archelaus, was dethroned. He wrote:
"Quirinius, a Roman senator who had gone through other magistracies, and had passed through them all until he had become consul, was appointed governor of Syria by Caesar and was given the task of assessing property there and in Judea."
So who was in charge as the assessor of property in Judea during the first census? Just as the Bible had said all along, Quirinius.
Argument 3: Like the above and, Census One v. Census Two?No so fast. Critics used this text for many years to make their case for a Bible that is unreliable. But no more. Today, there are a number of reasons for giving Luke the benefit of the doubt. Over and over (in references to 32 countries, 54 cities, and 9 islands) the doctor has proven himself to be a reliable historian, as demonstrated by famed scholar and archaeologist, Sir William Ramsey.
See ChristianAnswers' Web Bible Encyclopedia: What is a census?To date, the only census documented outside the Bible near this time under Quirinius is the one referred to by the historian Josephus (Antiquities XVIII, 26 [ii.1], which he says took place in 6 A.D.
But notice that Luke 2:2 says that the census taken around the time Joseph and Mary went down to Bethlehem was the first census taken while Quirinius was governor of Syria. This implies that there was a later census--most likely the one referred to by Josephus--which Dr. Luke would have also certainly known about.
There is good reason to believe that Quirinius was actually twice in a position of command (the Greek expression hegemoneuo in Luke 2:2which is often translated “governor” really just means “to be leading” or “in charge of”) over the province of Syria, which included Judea as a political subdivision. The first time would have been when he was leading military action against the Homonadensians during the period between 12 and 2 B.C. His title may even have been “military governor.”
A Latin inscription discovered in 1764 adds weight to the idea that Quirinius was in a position of authority in Syria on two separate occasions. There was definitely a taxing during this time and therefore, quite possible, an associated census, the details of which may have been common knowledge in Luke's time, but are now lost to us.
Scholars have advanced a number of other altogether viable explanations which would allow Luke's record (and therefore the Bible) to continue to be regarded as 100% trustworthy.
One more for good measure, but rather than quote the whole article, I'll just provide the link. This one is also from a Catholic source:
The Bottom LineWhen we encounter these skeptics of biblical inerrancy we must call them out on their ironically dogmatic stance. How can they be so sure (and dogmatic) in their arguments when valid counter arguments have been made? Do they just refuse to consider an argument which goes against their paradigm? These same people like to claim they have taken a rational position in opposing the Catholic Faith, but truly - especially in this case - their position, while making some valid points is highly irrational to proclaim their position as the ONLY (and non-falsifiable) position.