@lakshmi, thank you for sharing some of the cultural background and genre of Deuteronomy! That really helped to bring out both the role of faith in Old Testament blessings and the communal nature of many of the promises for me.
@alison, I also love the way you’ve captured the differences between Deuteronomy 28 and John 13!
I think those differences really get to the heart of the matter. It’s both about God redeeming a people for himself that he may dwell with them and about his accomplishing his purposes through covenantal relationship.
In Christ, we are no longer under the old covenant, but a new one (Luke 22:20), one that does not emphasize a physical kingdom, but instead the kingdom of God (John 18:36; John 17:15-24).
Though this kingdom may not be marked by the physical abundance of the land which came with the covenant blessings (Deut 28:3-12), it is marked by spiritual abundance even now (Gal 5:22-23; Col 3:12-17) as well as the contentment that flows from such abundance (Philippians 4:4-11). Not only did the nature of the kingdom change, but as you noted, the sign of the covenant has changed too so that it is our love for one another that marks us as belonging to Christ (John 13:34-35).
There is, however, still a lot of continuity between the kingdom blessings of the Old and New Testaments. While the arrival of kingdom of God began in Christ, it won’t be fully realized until the age to come (Eph 2:7, Matt 25:34). Yet it was ultimately to this eschatological kingdom that even the prophets in the Old Testament looked.
They longed for the eternal reign of David’s Offspring (Isaiah 11:1-9) and of the Son of Man (Daniel 7:8-14), that the kingdoms of this world would be defeated and God would reign in peace and justice.
While there may still be blessings in this life that come from following the Lord, such as Christian community as discussed here (Mark 10:29-31), or consequences for not walking in a manner worthy of God (1 Cor 11:29-31), such is not guaranteed, as Ecclesiastes poignantly points out (Ecc 8:14). Importantly, this is true even in the Old Testament - as the Ecclesiastes passage and the righteous poor that @lakshmi pointed out in Proverbs illustrate.
So, while physical blessings may come in this life as a result of following Christ, they are not guaranteed. And, as @alison summed up nicely, they are not the goal; I would argue that’s the case both in the Old Testament and the New. Finally, whether such blessings come or not, the eternal inheritance we will receive is far greater than any passing thing (2 Cor 4:17-18). As such, we look toward the eternal, storing up treasures in heaven (Matt 6:19-21) and longing to be with the Lord (2 Cor 5:8-9).