The basic argument is that the blessing of Abraham in Genesis 12:1-3 answers the curses of Genesis 3:14-19 point for point.
This argument about what is happening in Genesis 3 and 12 lays the groundwork for seeing the one in whom the blessings of Abraham are fulfilled as the one who overcomes the curses of Genesis 3, in particular fulfillment of Genesis 3:15.
I think this is exactly what Paul is talking about in Galatians 3:14, when he refers to the blessing of Abraham coming to the Gentiles in Messiah Jesus.
Thus, I would argue, with Thomas R. Schreiner, G. K. Beale, Richard B. Hays, and others, that Paul has rightly understood the Old Testament and presents powerful, indeed overwhelming arguments that all the promises of God are Yes in Jesus (2 Cor 1:20). Flowing from this, of course, would be the idea that we should learn how to read the OT from Paul and the other NT authors. After all, Jesus taught them how to read the OT (Luke 24:25-26, 44-49).
A revised version of the paper that I presented will appear in the next issue of Tyndale Bulletin, and you can read the summary of the essay here. Two years from now Tyndale Bulletin will allow me to post a PDF of the article. Until then, you’ll have to subscribe, visit a library with a subscription to Tyndale Bulletin, or check out the earlier version that I presented.
For related studies, see the following essays:
“The Messianic Music of the Song of Songs: A Non-Allegorical Interpretation,” Westminster Theological Journal 68 (2006) 331-45.
“The Skull Crushing Seed of the Woman: Inner-Biblical Interpretation of Genesis 3:15,” The Southern Baptist Journal of Theology 10.2 (2006), 30-54.
Paper Presented at the Tyndale Fellowship Conference Biblical Theology Study Group, July 2005: “The Virgin Will Conceive: Typology in Isaiah and Fulfillment in Matthew.” (this essay will appear in a forthcoming book from Eerdmans titled Built upon the Rock, ed. Dan Gurtner and John Nolland.