Indeed, when scholars apply the Negative Evidence Principle, it begins to look like the Jesus we know from the New Testament is the result of late first-century mythmaking.
The Negative Evidence Principle is, of course, not foolproof. It is not a proof in itself, but is rather a guideline, a good rule of thumb. How useful and reliable it is, of course, is subject to debate among logicians. Here's how the N.E.P. works - it states that you have good reason for not believing in a proposition if the following three principles are satisfied: First, all of the evidence supporting the proposition has been shown to be unreliable. Second, there is no evidence supporting the proposition when the evidence should be there if the proposition is true. And third, a thorough and exhaustive search has been made for supporting evidence where it should be found.
As for the first point, the only somewhat reliable, secular evidence we have for the life of Jesus comes from two very brief passages in the works of Josephus, a first-century Jewish historian. And Josephus was a prolific writer - he frequently wrote several pages on the trial and execution of individual common thieves, but on Jesus, he is silent except for two paragraphs, one of which is a known interpolation, and the other is highly suspect. Other references to Jesus in secular writings are ambiguous at best, or known to be later interpolations, or both. The earliest references to Jesus in the rabbinical literature come from the second century, even though known historical figures such as John the Baptist merit considerable discussion, even though his impact on Judaism was minimal. There are no references to Jesus in any of the Roman histories during his presumed lifetime. That he should be so thoroughly ignored is unlikely given the impact the gospel writers said he had on the events and politics of the Jewish kingdom.
So we have to turn to Christian literature for help.
At this point, caution is called for in examining first century Christian literature. This caution is made necessary by the fact that during this era, it was not considered wrong to write your own material and ascribe it to someone else, someone you consider your philosophical mentor, in whose name and style you are writing. Indeed, not only was this a common practice, but it was actually a skill taught in the schools of the day. This practice has made modern scholarship enormously difficult in dealing with who actually wrote the New Testament books and when. The problem, though difficult, is not insoluble, and modern scholarship has developed techniques which have been applied to early Christian writings, to find out who is saying what, when and why. When these techniques are applied to these early Christian writings, the results have been quite surprising.
The writings of Paul accepted as genuinely his (Galatians I and II and Thessalonians I and II, Corinthians, Romans, Philemon, Phillipians, and possibly Colossians) are by far the most pristine of any early Christian literature we have. They were probably written beginning in the fifth decade of the first century - well after the events of Jesus' life. When the letters are examined in isolation, it becomes apparent that Paul was ignorant of the doctrine of the virgin birth, that he never spoke in terms of having lived in Jesus' time, nor does he mention that any of his mentors were contemporaries of Jesus, nor that Jesus worked any miracles and he appparently did not associate the death of Jesus with the trial before Pilate. Only in Galatians 1:19 does he make reference to a contemporary Jesus, and then only in terms of James being the "Lord's brother." The use of the term "Lord's" even makes that single reference somewhat questionable to scholars, as the word "Lord's" did not have currency until the late 2nd. century. So the Pauline letters, at least the reliably Pauline letters, aren't good witnesses for a Jesus of the first half of the first century. What makes this particularly interesting, is that other non-Canonical early Christian pre-Gospel literature make the very same omissions.
Later Christian writings were written well after the events they describe, none earlier than at least the seventh decade at the earliest. And none of them are known to have been written by the authors to which they are ascribed. Most are second or third-hand accounts. There was plenty of time for mythmaking by the time they were written, so they're clearly not reliable witnesses.
The next stricture of the Negative Evidence Principle is that there isn't any sound evidence where there should be, and here again this stricture is met. First, there are no records whatever of Jesus' life in the Roman records of the era. That's surprising, since he stirred up so much unrest, at least by Biblical accounts. There at least ought to be a record of his arrest and trial, or some of the political notoriety the gospel writers describe. Yet the Roman histories are silent, even though they are quite thorough (Flavius Josephus alone wrote dozens of volumes, many of which survive, and he is far from the only historian of Palestine in this period whose writings have survived in some form). Second, as mentioned, there is no reliable account in Josephus.
Josephus was a historian who was so very thorough he would write a three page history of the trial and execution of a common thief, and wrote extensively about John the Baptist, but on Jesus, his two small references are seriously doubted by scholars as being genuine. Unfortunately, the writings of Josephus have come down to us only through Christian sources, none earlier than the fourth century, and are known to have been revised by the Christians. There are a number of reasons why the two references in Josephus are doubted: As summarized by Louis Feldman, a promient Josephus scholar, they are, first, use of the Christian reference to Jesus being the Messiah is unlikely to have come from a Jewish historian, especially from one who treated other Messianic aspirants rather harshly; second, commentators writing about Josephus earlier than Eusebius (4th Cent. C.E.) do not cite the passage; third, Origen mentions that Josephus did not believe that Jesus was the messiah. There is a full account available on the Internet that describes the whole long list of problems with the "Testimonium Flavium" as scholars call it.
The earliest secular literary evidence for a religion based on the man we call Jesus comes from many decades after Jesus' supposed death (from about 70 C.E.). Why, if he had as much influence, and caused as much a stir as the Bible says he did, do we not know of him at all from reliable, contemporary testimony?
The third stricture of the N.E.P. holds that we must have conducted a thorough and exhaustive sweep for evidence where there should be evidence. Indeed, thousands of scholars, religionists, crusaders, apologists and skeptics alike have searched for such evidence since the earliest days of the Christian era. That they haven't found any reliable evidence that should have been there says that the third stricture has been clearly satisfied.
So based on the Negative Evidence Principle, we have good reason to doubt the historicity of Jesus and that lack of reliable evidence suggests no good reason to accept it.