Continuing some of my writing from Sunday...
... If Dunn is correct that Paul primarily has works of the Jewish Law in view, particularly those actions that distinguished Jew from Gentile, then the issue is alleviated somewhat. Then Paul was never thinking about works of love or a life free of murder or sexual immorality when he declared that Jews and Gentiles are not justified by works of Law. Rather, he was primarily thinking about works like circumcision, food laws, Sabbath observance, and so forth.  This ambiguity in Paul’s language of Law goes a long way toward explaining what might otherwise seem like inconsistencies. How could a Gentile possibly demonstrate the Law written on their hearts (Rom. 2:15) unless some of Paul's uses of the word law referred to a core of the Jewish Law that did not include those boundary markers than distinguished Jew from Gentile? Other instances then had these boundary markers as their primary referent.
A second ameliorating factor in explaining Paul's rhetoric of faith versus works against a revised sense of his Jewish background is the strong possibility that at least some of his references to the "faith of Jesus Christ" refer not to human faith directed toward Christ but to the faithfulness of Jesus Christ himself. The name of Richard Hays is not usually invoked when presenting the new perspective on Paul. He is rather associated most strongly with the resurgence of a particular interpretation of the phrase, pistis Iēsou Christou, in passages like Romans 3:22 and Galatians 2:16.  Reviving and re-presenting an older suggestion, Hays argued that this phrase should be understood as a reference to the "faith of Jesus Christ," his faithfulness to the point of death, rather than to faith in Jesus Christ, as the phrase had traditionally been understood. It is a question of whether Jesus in this phrase is an objective genitive—trust of Christ—or a subjective genitive—faith of Christ, understood as Christ's faith. Hays' revival of this interpretation was not a direct result of Sanders’ work on Judaism nor of Dunn and Wright’s versions, so it is understandable that it is often not included in discussions of the new perspective.
Another reason why the pistis Christou debate is often not connected to the new perspective is the fact that James Dunn, one of the key players in the new perspective, is Hays' most notorious sparring partner on the issue. Neither Sanders nor Dunn agree with Hays' reading of the key passages. On the one hand, Hays does not deny that faith in Jesus was part of Paul's theology. Indeed, part of his argument in relation to the interpretation of Galatians 2:16 is that Dunn’s interpretation implies an extensive redundancy in this verse. Paul's statement amounts to three consecutive mentions of faith in Christ: "knowing… through faith in Jesus Christ, even we have put faith in Christ Jesus in order to be justified through faith in Christ." By contrast, in Hays’ interpretation, only the second instance, the expression εἰς Χριστὸν Ἰησοῦν ἐπιστεύσαμεν (“on Christ Jesus we have believed”), refers to faith directed toward Christ Jesus.
If Hays' interpretation is at least in part correct, our picture of earliest Christianity does seem even more integrated with its Jewish precedents than even in Dunn's reconstruction. Paul’s theology, for example, turns out to be theocentric more than Christocentric. God rather than Christ becomes the primary object of faith (cf. 1 Thess. 1:8). I have argued elsewhere that Paul may, in effect, argue "from Hays to Dunn." In this reconstruction, the initial sense of διὰ πίστεως Ἰησοῦ Χριστοῦ in both Romans 3:22 and Galatians 2:16 would be "the faithfulness of Jesus Christ," perhaps a shorthand for a common Christian belief that the faithful death of Jesus was an atonement for the sins of Israel. Paul may then have used the ambiguity of the genitive phrase in order to suggest that the fundamental principle of justification was faith, now contrasted with works of Law in a more ethnocentric sense.  This reading combines the strengths of both Hays and Dunn's arguments.
In this revised perspective on Paul, Paul conflicts with other Jews primarily on the significance of what we might call the ethnic particulars of the Jewish Law, those boundary aspects of the Law that most differentiated Jew from Gentile. This is an argument generated from practice, namely, whether Gentiles must be circumcised and whether Jewish believers can have table fellowship with Gentile believers. These arguments are simply ideological proxies for real people that Paul believed must be fully included within the people of God.
Paul argues that faith is the more basic principle than these boundary practices. He uses the example of Abraham, who was justified before he engaged in the Jewish boundary marker of circumcision (e.g., Rom. 4:9-10). While Paul's Jerusalem brothers and sisters agree that the faithful death of Christ as essential to justification, in Paul's view they overrate the significance of Jewish particulars in the Law in the equation of righteousness. Paul radicalizes the principle--even Jews are not established as right before God by their keeping of boundary markers. The essence of rightness before God is faith, and there is a core to the Law that even Gentiles can keep, a circumcision of the heart...
 As Dunn and Wright have both demonstrated, 4QMMT among the Dead Sea Scrolls suggests that the phrase "works of Law" especially referred to inter-Jewish debates over how to keep the Jewish Law. See Dunn, "4QMMT and Galatians" in New Perspective, 339-345 and Wright, "4QMMT and Paul: Justification, 'Works' and Eschatology," in Pauline Perspectives, 332-355.
 πίστις Ἰησοῦ Χριστοῦ. His primary work in this regard is, The Faith of Jesus Christ: The Narrative Substructure of Galatians 3:1-4:11, 2nd ed. (Grand Rapids: Eerdmans, 2002).
 "2 Corinthians 4:13 and the πίστις Χριστοῦ Debate," CBQ (2008): 524-37.