There is a very interesting essay In the latest issue of the Journal for the Study of the Historical Jesus by John H. Elliott, "Jesus the Israelite Was Neither a 'Jew' nor a 'Christian': On Correcting Misleading Nomenclature." This is the abstract of the essay: 

"Distinguishing between insider and outsider groups and their differing nomenclatures is essential for accurate interpretation and translation.  Jesus and his earliest followers, evidence demonstrates, were called ‘Israelites’, ‘Galileans’, or ‘Nazoreans’ by their fellow Israelites.  ‘Israel’, ‘Israelites’ were the preferred terms of self-designation among members of the house of Israel when addressing other members—not Ioudaios, ‘Jew’ or ‘Judaism.’ Modern interpreters and translators of the Bible, it is argued, should respect and follow this insider preference. Ioudaios, an outsider coinage, is best rendered ‘Judaean,’ not ‘Jew’, to reflect the explicit or implied connection with Judaea. It was employed by Israelites when addressing outsiders as an accommodation to outsider usage. The concepts ‘Jew,’ ‘Jewish,’ and ‘Christian’ as understood today are shaped more by fourth century rather than first century CE realities and hence should be avoided as anachronistic designations for first century persons or groups. Use of ‘Christian’ is best restricted to its three NT appearances.  The use of appropriate nomenclature is crucial for minimizing historical and social inaccuracies and misunderstandings."

Much recent historical Jesus research (i.e., the past  30 years) has emphasized that Jesus was a Jew, and rightly so. This essay is not attempting to do away with this emphasis, but rather point out that "Jew" as primarily an outsider label, while "Israelite" was the primary insider label. The essay is in JSHJ 5.2, July 2007. If your library does not subscribe to it (either in paper or electronically), then you can get it here, but it might cost a little.

As a side note, I was giving a lecture a couple of weeks ago introducing the apostle Paul, and I was talking about influences from his background. I stressed, of course, that Paul was a Jew. And for my evidence I had my students turn to Paul's description of himself in Philippians 3:5. What caught me was that Paul's self-designation was actually that he was "of the people of Israel."