You have a point but your example of Kim Jong Il is, I suggest, misleading.
Yes, the claims made about Jesus are indeed extraordinary and it is perfectly natural to be suspicious about the veracity of these claims. But the claims about Kim Jong Il take on their comical air at least in part due to the nature of the man himself - whereas Kim Jong is seen, and likely will continue to be seen, as a decidedly negative figure, Jesus continues to be lauded as one of the greatest human beings who has ever lived. Do not misunderstand me: I am not saying this gives we Christians a "pass" with respect to needing to explain the miracles: I am simply pointing out that your example gains at least some of its rhetorical oomph due to the wrenching contradiction between the claims about Kim Jong and his image as a buffoon.
I would say this, too, in defense of believing the Jesus stories: Jesus emerged in a setting where his contemporaries were expecting something completely different from a Messianic figure than what we see in the gospel accounts. So one could argue that if people were going to invent stories, they would have invented very different stories (for example, they would never have their Messianic figure dying on a cross). So the general principle here is this: when one encounters extraordinary claims in a setting where there is a case to be made that such claims would hard to invent given the matrix of expectations, then the likelihood the claims are true is strengthened somewhat. Of course, I am aware the gospels were written decades after the alleged events and it is therefore plausible that the authors had time to re-work their worldview and "invent" the miracle accounts accordingly.
The world remains a mysterious place with profound mysteries still before us (e.g. the origin of the universe, the phenomenology of human consciousness). So while I agree it is a "stretch" to accept the Jesus accounts, I don't think we have warrant to dismiss them so easily as I suspect many do.