Christian apologists often complain about New Testament critics who bring an a priori rejection of the supernatural to their studies of the New Testament. The underlying rationale, I take it, is that such a presupposition will determine a non-supernatural historical reconstruction of Jesus before they even begin their historical investigations. But if the historical Jesus turns out to be the miracle-working, resurrected Son of God that conservative Christians take him to be, such an assumption will lead them to construct a historically inaccurate conception of Jesus.
I agree with them in this regard: one shouldn't assume what can or can't be true on empirical matters before one even begins one's investigations. Although it's probably unavoidable that we bring assumptions about reality to all of our empirical inquiries, we should hold them tentatively, and allow them to be altered in light of our findings.
Of course, this assumes that supernatural events, if they occur, are capable of empricial detection, but I grant that they are detectable, at least in principle (I say this as someone who has read his Hume).
I also agree with them that there are some NT critics who do reject the supernatural a priori (e.g., the members of the Jesus Seminar, Gerd Ludemann, etc.). Having said that, however, I'd like to make three points with respect to naturalism, a priori commitments, and NT studies.
First, many New Testament critics do not assume that supernatural events do not or cannot occur; rather, they have principled reasons for thinking that, even if they do occur, the evidence for such events is never sufficient to establish their occurence. There are two ways to construe the 'never' here: never in practice and never in principle (both construals go back, of course, to Hume's famous essay "Of Miracles" in his Enquiry Concerning Human Understanding). Now one may disagree with their arguments on these matters (I tend to think that Hume's "in principle" argument is too strong, although I think his "in practice" argument has considerable force), but that's not the point. Rather, the point is that apologists too often attack straw men here, viz., by attributing to NT scholars a metaphysical basis for their conclusions, when in fact they're often based on epistemological considerations.
Second, although some NT critics do base their non-conservative conclusions about Jesus in particular or the New Testament in general on an a priori rejection of the supernatural, they need not do so. In fact, many don't. Indeed, there are plenty of NT scholars who are also serious Christians, yet who nonetheless reject the doctrine of inerrancy, based on their research. In other words, non-conservative views of Jesus and/or the New Testament are supportable merely from applying ordinary historical methodology. For example, one can see how the geneologies and pre-birth narratives in Matthew and Luke contradict both each other and established historical fact in order to make theological points. The same goes with John versus the synoptic gospels on the day and time of Jesus' crucifixion: John changes it in order to fit his theological theme of Jesus as the Passover "Lamb of God" (I know that inerrantists argue against these discrepancies. I have no desire to argue with them in vain. I merely ask them to read a sufficiently representative sampling of NT scholarship outside of their conservative circles). Also, once one does their source-critical homework, they can see how, e.g., Matthew and Luke modified the portrait of Jesus they inherited from Mark and Q, and how John went even further. Thus, a non-conservative account of Jesus in particular and the New Testament in general often results from ordinary, non-controversial use of source criticism, redaction criticism, and the criteria of authenticity -- it need not be based on an a priori rejection of the supernatural. Complaints about "ruling out the supernatural a priori" are therefore something of a red herring.
Finally, if some NT critics are guilty of an a priori commitment to naturalism, many conservative NT scholars are guilty of an a priori commitment to inerrancy. Yet many apologists don't seem to mind when the latter determines the conclusions of conservative NT scholars. This leads one to question the sincerity of apologists in their criticisms of a priori commitments creeping into NT scholarship. For again, the basis of their criticism appears to be that such a priori commitments are liable to result in an inaccurate historical reconstruction of Jesus, should the person of Jesus turn out to be in conflict with those commitments. But if that is the basis of their criticism, then they should be equally diligent in their criticisms of conservative scholars who have an a priori commitment to inerrancy -- and to a conservative view of Jesus in particular and the New Testament in general. In other words, the potential danger here is not naturalistic a priori commitments, but a priori commitments per se.
But it's hard to deny that there is an a priori commitment to inerrancy among the majority of conservative NT scholars. For one thing, many of them work at conservative seminaries, where one must subscribe to and even sign extremely conservative doctrinal statments in order to obtain and keep one's job. Such scholars can't let an admission of errancy through the door, no matter what the data, and no matter what sort of convoluted just-so stories are required to reconcile a given set of biblical texts. Thus, it's a bit odd to hear apologists complain about a priori committments determining one's portrait of Jesus, when their own a priori committments determine their own portrait of Jesus.
To sum up: Christian apologists have a point worth hearing when they criticize certain NT critics for bringing an a priori commitment to naturalism to their studies. For one should let the empirical data about Jesus and the NT materials speak for themselves, lest one's conclusions be determined from the get-go, quite possibly distorting the data in the process. However, the apologists have failed to see that the point about a priori assumptions is a perfectly general one, and can't be limited to naturalism. And this entails that conservative NT scholars need to abandon a priori assumptions about inerrancy and orthodoxy when they come to their study of the empirical data, lest they, likewise, allow their assumptions to determine their conclusions from the get-go, quite possibly distorting the data along the way. The lesson is that all sides of the debate should hold their theoretical commitments tentatively, not forcing the pieces of evidence to fit within them when the fit is unnatural. Rather, one's assumptions should be malleable, and even disposable, thereby allowing the data to speak to us clearly, unmuffled.
 Examples include Raymond Brown, Dale Allison, James D.G. Dunn, John Meier, and Luke Timothy Johnson.
 For many examples of such just-so stories, see, e.g., Craig Blomberg's The Historical Reliability of the Gospels, Norman Geisler's When Critics Ask, and Gleason Archer's Encyclopedia of Bible Difficulties.