I think it quite likely that Jesus is an offshoot of an ancient version of Yahve depicted along the lines of Baal, Osiris, Dionysus or Attis: a heavenly hero or king who won his divine throne by defeating a dragon who initially devoured him, but then yielded to the resurrected savior. At some point, institutional consolidation, factional polemics against spiritualists like the Gnostics, led church officials to historicize their Jesus as a figure of recent history....
Nor is it clear that whatever new element lent Christianity its new nametag must have had much to do with ostensible events in Jewish Palestine. One can understand how various Mediterraneans of various nationalities would have been happy enough to add a new name, Jesus, to their portfolio/pantheon of initiation deities. (First Corinthians 8 seems to be trying to stop such ecumenical henotheism, presupposing its practice.) It is not so easy to picture Gentiles giving a fig over whether a recently executed man named Jesus had really been the theocratic king of Israel. What concern was that of theirs?...A Jesus mystery religion with its sacramental meal of wine (like the Dionysiac blood) and bread (like the Osirian flesh) required no historical founder, recent or remote, any more than the similar faiths of Isis, Mithras, Attis or the rest. (in James Beilby and Paul Eddy, edd., The Historical Jesus: Five Views [Downers Grove, Illinois: InterVarsity Press, 2009], pp. 179-180)
In later generations, did Christianity radically redefine itself, in a manner comparable to what Price is suggesting, whenever it came into contact with opposition from groups like the Gnostics? Was Christianity radically redefined in response to later Gnostics, modalism, Arianism, etc.? Did the Christians of later generations collectively rewrite the gospels whenever such groups came along, perhaps placing Jesus in a different century, changing the events that occurred during His life, discarding previous gospels and adding new ones, etc.? Or did such radical changes only occur early on, then were persistently avoided? Why don't we see a Chinese Jesus placed in the third century B.C. in order to respond to the Gnostics of Irenaeus' day, a Spanish Jesus placed in the second century A.D. to respond to the Arians, etc.? If the beliefs surrounding early Christianity were so flexible, why is there not nearly as much flexibility in the generations following the period Price is speculating about? High flexibility of belief could be closely followed by high inflexibility, but that's not the best explanation of the evidence. High inflexibility all along makes more sense of the data.
How would the early Christians have gotten so many people, including enemies of Christianity, to go along with such a major redefinition of the religion? As second-century disputes among Christians illustrate (the dispute over second repentance, the Quartodeciman controversy, etc.), it would be difficult to even get all mainstream Christians to go along with a change like the one Price is suggesting. Getting people like Josephus, Tacitus, and Trypho to go along with it would be even more difficult.
A common skeptical reaction at this point is to argue that the early Christians may have distorted the historical record, such as by destroying or altering documents, so that we can't trust what that historical record tells us about sources like the second-century Christians and Tacitus. For a discussion of some of the problems with such an objection, see here, including the comments section of the thread.
Price refers to a reaction against "spiritualists like the Gnostics", but such spiritualists were already acknowledging more than Price's theory would suggest. If Jesus didn't exist, then spiritualists would have had an interest in saying so. Instead, we find them acknowledging that Jesus appeared to exist, but arguing that He wasn't physical. For example, Ignatius of Antioch writes in response to such spiritualists:
"He [Jesus] was truly of the seed of David according to the flesh, and the Son of God according to the will and power of God; that He was truly born of a virgin, was baptized by John, in order that all righteousness might be fulfilled by Him; and was truly, under Pontius Pilate and Herod the tetrarch, nailed to the cross for us in His flesh....Now, He suffered all these things for our sakes, that we might be saved. And He suffered truly, even as also He truly raised up Himself, not, as certain unbelievers maintain, that He only seemed to suffer, as they themselves only seem to be Christians. And as they believe, so shall it happen unto them, when they shall be divested of their bodies, and be mere evil spirits....But if these things were done by our Lord only in appearance, then am I also only in appearance bound. And why have I also surrendered myself to death, to fire, to the sword, to the wild beasts? But, in fact, he who is near to the sword is near to God; he that is among the wild beasts is in company with God; provided only he be so in the name of Jesus Christ. I undergo all these things that I may suffer together with Him, He who became a perfect man inwardly strengthening me." (Letter To The Smyrnaeans, 1-2, 4)
In other words, people like Ignatius weren't the only ones who affirmed that Jesus seemed to exist on earth. The spiritualists Ignatius is responding to also acknowledged that fact. The difference was over whether Jesus' apparent existence was physical or only appeared to be physical. The spiritualists acknowledged that there was an appearance of existence that had to be explained. Not only do the mainstream Christian sources contradict Price, and not only do mainstream opponents of Christianity like Josephus and Tacitus contradict him, but so do spiritualists like the Gnostics. Price's speculations are grossly inconsistent with the historical record, inconsistent with both Christian and a variety of non-Christian sources. (For some additional evidence from Ignatius and other early sources, including more evidence that I'm interpreting Ignatius correctly, see Allen Brent, Ignatius Of Antioch [New York, New York: T & T Clark International, 2009] and John McGuckin, The Westminster Handbook To Patristic Theology [Louisville, Kentucky: Westminster John Knox Press, 2004], pp. 105-106. Concerning the widespread Gnostic and heretical acceptance of the gospels, despite their efforts to reinterpret those documents, see here.)
Notice, too, that these early spiritualists don't just acknowledge that Jesus appeared to exist. Rather, they even acknowledge that He appeared to experience what mainstream Christians were claiming He experienced physically. As Ignatius' comments above illustrate, the spiritualists acknowledged that Jesus "seemed to suffer". Apparently, Ignatius emphasizes that Jesus truly was born of a virgin, suffered, rose from the dead, etc. because the spiritualists were saying that He only appeared to experience such things. Not only did these spiritualists corroborate the fact that Jesus seemed to exist, but they even corroborated the fact that He seemed to experience the events that mainstream Christians were claiming He experienced (the virgin birth, crucifixion under Pilate, etc.).
And if, as Price suggests, the early Gentile Christians didn't "give a fig" about Jewish religious concepts, then why would a mostly Gentile Christianity, or one interested in appealing primarily to Gentiles, fabricate historical accounts that are as Jewish as the New Testament documents? Is a religion that started with pagan mystery concepts less than a century earlier the best explanation for a long series of founding documents that are so Jewish, documents that repeatedly condemn paganism and refer to the ignorance and corruption of those who follow pagan religions?
Price ignores what the New Testament documents themselves say about why Gentiles accepted a Jewish religion, particularly one as despised and persecuted as Christianity. There does indeed need to be something sufficient to explain such an unlikely scenario, and the explanation given by the New Testament is one that Price and other critics don't like. The New Testament documents, as early as Paul's letters, repeatedly appeal to evidential categories like fulfilled prophecy, eyewitness testimony, and miracles performed by Jesus and the apostles. Paul makes much of his own performance of miracles (Romans 15:19, 1 Corinthians 2:4, 2 Corinthians 12:12, Galatians 3:5). It should be noted that Paul sometimes refers to his miracles in contexts in which his authority was being questioned and among people who were skeptical of him for other reasons (the Corinthians and the Galatians). In Romans 15, Paul refers to such miracles as characteristic of his ministry in general. He refers to his apostolic status derived from what he eyewitnessed (1 Corinthians 9:1), and he cites the testimony of other witnesses (1 Corinthians 15:3-11). Such appeals to evidence are found many times in the New Testament, from a variety of authors and in a variety of contexts, and those themes are repeated many times from the earliest patristic documents onward. The claims are sometimes corroborated by non-Christian sources, as we see with Jesus' performance of apparent miracles and His empty tomb, for example.
Under Price's view of things, both the earliest Christian sources and the earliest non-Christian sources frequently arrived at radically incorrect beliefs, often agreeing with each other over those wrong beliefs. Multiple groups that had an interest in mentioning the errors of Christianity that Price alleges, and were in a position to know about those errors, not only didn't mention the errors in our extant documents, but instead repeatedly corroborated what the Christians were saying.