It all depends on what one means by a reasonable doubt.  If by a reasonable doubt, one means that a person can suggest sane, sensible reasons why a certain saying attributed to Jesus in the Bible is less likely to represent what he probably said (or did) than some other saying (or deed), then the answer is, of course, there can be such doubts.  That's what the entire "historical Jesus" enterprise in scholarship is all about.  But if one means that they think there are no good historical reasons for trusting the gist (skeleton, major contours, basic outline, however one cares to phrase it) of the New Testament Gospels, especially Matthew, Mark and Luke, and especially where they agree with each other, then historians would have to demur.  There is an unbroken tradition of literature that has been preserved down through the centuries that makes understanding the historical Jesus, or the historical Alexander, or the historical Socrates, etc., a very doable task--within limits--in ways that is not the case when a historian tries to study a figure from the remote past that hasn't had the impact on civilization that characters like these have had.