I was surprised to find out that this is not a widely used argument. Defenses for the existence of Jesus tend to focus on extra-biblical evidence. However, a significant portion of apologists use both biblical and extra-biblical evidence. For example, at the 4truth.net apologetics web, an article by the ancient historian Paul Maier explicitly appeals to both biblical and extra-biblical evidence on this issue:
By 'sacred' evidence, Maier means evidence from the sacred scriptures, the Bible (esp. the New Testament).
A couple of Apologetics websites provide some illumination as to why the focus is usually on extra-biblical evidence. On the Stand To Reason apologetics web, I found the following explanation:
Sometimes as Christians, we find ourselves trying to defend our faith by appealing to the evidence of the Bible. We believe the Bible to be an accurate, reliable eyewitness account of the life of Jesus, and we have good reason to believe this to be true (see our Power of the Book section!) But let’s face it; there are many people in our lives who just won’t accept the Bible as an eyewitness account. They are looking for something more. They want to know if anyone OTHER than the first believers wrote anything about Jesus, and they want to know if these other accounts of Jesus line up with what the Bible says about our Savior.
by J. Warner Wallace
by an unknown author (no indication given of who founded the website or authored the articles)
Here the Christian apologist anticipates a specific objection to the use of the NT as evidence for the existence of Jesus: this would be "using the Bible to prove the Bible." That sounds like an objection that using NT based evidence would be circular reasoning or would involve the fallacy of begging the question. The apologist responds by indicating that the NT evidence would be perfectly acceptable, assuming that the NT books used were "written by eye witnesses of both Jesus and the apostolic ministry".
That hardly seems an adequate response to the charge of begging the question. If particular books of the NT (such as the Gospels) are assumed to have been written by an "eye witness of...Jesus", then one is assuming that there was in fact a Jesus to be seen and heard. But that is the very question at issue: Was there in fact a flesh-and-blood Jesus, a Jewish preacher who lived and travelled around Galilee in the first half of the 1st Century to be seen and heard?
The assumption that, for example, the Gospel of Matthew was written by an eye witness of the ministry of Jesus appears to beg the question, because this assumes that there was in fact a flesh-and-blood Jesus who had a ministry which could be observed by an eye witness. If one must first establish the existence of Jesus in order to show that an author of some book was an eye witness of the ministry of Jesus, then using the assumption that the author of a certain book was an eye witness of the ministry of Jesus to prove that a flesh-and-blood Jesus really existed would be reasoning in a circle.
Although the unidentified Christian apologist put the phrase "using the Bible to prove the Bible" in scare quotes, indicating that the apologist did not agree with this objection, the objection is not so easily cast aside. This objection deserves more attention, and it will be considered more thoroughly in future posts in this series.
In my brief survey of Christian apologetic web sites, I did however, come across a few that focused on NT evidence for the existence of Jesus. One such web site is the Christian Apologetics & Research Ministry (CARM). On that site I found an article by Matt Slick, the founder of CARM, which focuses on NT evidence for the existence of Jesus:
Was Jesus just a myth?
In reality, a person must ignore a great deal of evidence establishing the historic accuracy of the gospels. In other words, the Bible...alone is sufficient evidence that Jesus lived, whether or not the critics want to admit it. But making this claim doesn't establish it as fact. So, let's look at reasons why Jesus is not a mythical creation, but an actual man who lived in Israel.
from "Was Jesus just a myth?"
At the CompellingTruth.org apologetics web, I found an article that also focused on NT evidence for the existence of Jesus:
Did Jesus exist? Is there historical evidence that Jesus existed?
Typically, when historical evidence of Jesus' existence is sought, what is meant is evidence "outside of the Bible." But the Bible is a reliable historical source of evidence for the existence of Jesus and nothing in the Bible has ever been discredited by secular historians. In terms of ancient evidences, writings less than 200 years after events took place are considered very reliable evidences and the entire New Testament was written within 100 years of Jesus' death. ...
from "Did Jesus Exist?"
by an unknown author
While this article focuses on the NT evidence, it does also mention evidence from outside the NT (e.g. Josephus and Lucian), so it does not stick exclusively to NT evidence.
At the web for the Warren Apologetics Center, I found an article that spells out an argument based on NT evidence.
The Logic of the Case for Christ
1. If (1) A existed and if (2) A said that B existed, and if (3) A is credible, then B existed.
2. (1) A existed, and (2) A said that B existed, and (3) A is credible.
3. Then B existed.
In a modus ponens argument, the logical connective represented by the words "If___, then___" drops out, so that the conlcusion is simply the consequent of the conditional statement:
1. IF P THEN Q.
There is no "THEN" in the conclusion here; that is the whole point of a modus ponens; out of the complext conditional statement in premise (1) we get a conclusion (3) that this just a simple proposition.
But setting aside the amazing ignorance of logic in an article with "The Logic of..." in the title, it is clear that the argument outlined here is focused on evidence from the NT for the existence of Jesus.
Finally, I should point out that while Paul Maier's article on the 4truth.net apologetics web uses both NT evidence and extra-biblical evidence, Maier specifically states that the NT evidence would be sufficient by itself:
From the internal, biblical evidence alone, therefore, Jesus' existence is simply categorical.
So, I conclude that some Christian apologists, including the founder of the Christian Apologetics & Research Ministry (Matt Slick), focus primarily on NT evidence for the existence of Jesus, and that some Christian apologists, including the ancient historian Paul Maier, who use both NT evidence and extra-biblical evidence believe that the NT evidence is sufficient by itself to establish the existence of Jesus.