Is there any serious person who actually denies that there was a man who called himself Jesus, claimed he could perform miracles, and was crucified?
It's a fringe position in New Testament scholarship, but a few notable proponents do exist: namely the aforementioned Carrier and Price, who have become known for advancing it on the Internet. Mythicism was a much more mainstream belief among scholars in the late 18th to early 20th century, but research since the 1970s has increasingly supported the historicist view.
The main mythicist argument is that the earliest Christian writings (i.e., the Pauline epistles) do not contain any biographical information about a historical Jesus, even when it would be convenient for Paul to reference examples or justification from Jesus' life. Paul is explicit that the gospel he teaches does not have an earthly origin, rather being revealed to him personally (Galatians 1:11). He preached this gospel for three years before meeting Peter and James (Galatians 1:18).
Carrier posits that Paul's epistles likely thus do not refer to a historical Jesus but a divine Son of God who was crucified and resurrected in a spiritual realm, similar to other "dying-and-rising" deities common to Antiquity. The Gospels were then later written to "concretize" Jesus and place him within human history.
My main issue with Carrier's thesis is that Paul's Jesus has several characteristics that we wouldn't expect had he been a Jewish myth. First Century Jews would not have invented a trinitarian Jesus who is coextensive with God the Father, nor would a Jewish "rising-and-dying" diety have been killed in cosmic recreation of a Hellenistic crucifixion.
