The following quotes are from ‘The Obedience of Faith’ A Pauline Phrase in Historical Context by Don Garlington. The work of Garlington and others like him has proven invaluable in determining the structure of the Christian faith and covenant by providing a historically accurate picture of Second Temple Judiasm. This picture shows that Judaism was not primarily a legalistic religion and this understanding is necessary for correct interpretation of the New Testament.
From the Preface, page 1:
The (phrase) ‘obedience of faith’ is primarily a commitment to God’s covenant as embodied in the totality of the law of Moses; disobedience correspondingly, is predominately apostasy from the covenant. Because of this denotation of the ‘obedience of faith’ in Jewish theology, Paul’s phrase assumes the character of a manifesto that the nations can now participate in God’s new covenant apart from becoming or remaining Jewish.
From page 233:
The obedience of God’s people, consisting in their fidelity to his covenant with them, is the product of a prior belief in his person and trust in his word. Far from being a quest for meritorious self-justification, faith’s obedience is the appropriate response of Israel, the covenant partner, to the election grace and mercy of God. [footnote: ‘The obedience of faith,’ then, is another way of saying ‘covenantal nomism’.]
From page 251:
The very notion of righteousness entails a comprehensive assessment of one’s place in God’s covenant: neither the OT nor Paul know of a righteousness which is merely forensic.
From the Conclusion, page 254
‘The obedience of faith’ is a phrase coined by Paul in his dialogue with both Judaism and Jewish Christianity; in it he gives voice to the intention of his missionary labours, viz., to make people of all nations faithful covenant-keepers by virtue of trust in Christ and union with him. The historical context of Paul’s mission . . . dictates . . . [that] he did so in deliberate interaction with the traditional viewpoint that faith’s obedience is impossible apart from the assumption of responsibility for the totality of the law of Moses.
The evidence is mounting that the Christianity of the first century was not characterized by an antithesis between “gospel” and “law” as Luther and many of the Reformers argued. Instead, the cultural context indicates that the writings of Paul (and the rest of the NT writers) are better and more accurately cast in the light of the question: Must one become a Jew in order to be a Christian?