Joel B. Green, Provost, Dean of the School of Theology, and Professor of New Testament Interpretation at Fuller Theological Seminary contributed a chapter to the recent book Evolution and the Fall addressing just this question. Green finds the primary significant passages in Paul (of course) and James. The latter is unusual and gives something of a different emphasis to his discussion than that found in the work of most other scholars.
Before digging into Paul and James, Green looks other Second Temple works, Life of Adam and Eve, 4 Ezra, 2 Baruch, and Biblical Antiquities. Although the sin of Adam and Eve plays no significant role in the Old Testament after Genesis 3, it had become a topic of speculation in the Jewish world. This provides a context for Paul and James. Green concludes: “Paul and James would have swum in the same theological pond as the Jewish authors … and their contributions can be read in dialog with perspectives like those of 4 Ezra or Biblical Antiquities.” (p. 106)
Green’s summary of the pond: Adam’s disobedience results in human mortality but each individual human remains responsible for his or her own sin. “In short, when sin’s origins are discussed, Jewish writers of the Second Temple period refer to human choice even as they speak of Adam’s (or Adam and Eve’s) influence. Sin is not compulsory, even if its ubiquity might suggest its inevitability.” (p. 105)
So what about Paul and James?
Paul understands sin as “more a power from which humans need to be liberated than individual wrongful deeds for which humans require forgiveness.” (p. 106) This is particularly clear in Romans 5-7.
Sin “entered the world” (Rom. 5:12), where it exercised power reminiscent of a master-slave or king-subject relationship. Humans are “controlled by sin” (Rom 6:6), the aim of sin is to “rule your bodies, to make you obey their cravings [epthymia]” (Rom. 6:12, my translation), people present “parts of their body to sin as weapons to do wrong” (Rom. 6:13), and people comport themselves as slaves to sin (Rom. 6:16). Whereas in the Life of Adam and Eve, cravings give rise to sin, for Paul the opposite is the case: sin produces all kinds of cravings. And whereas in the Second Temple literature we surveyed obedience to the law was the means for countering cravings and sin, for Paul the law is an instrument sin uses to cultivate those cravings (epthymia; Rom. 6:12; 7:7-8). The baptized were formerly enslaved to sin, but they are now liberated from its dominion (Rom. 6:17-18, 20, 22). (p. 107)