Sections of this week’s portion figure prominently in Arguing with God: A Jewish Tradition, by Anson Laytner (Northvale, NJ: Jason Aronson, 1990).
Anson explores rabbinic use of Moses’ arguments (p.49ff). He describes liturgical use of verse 32:12 — “turn from Your fierce wrath, and repent the evil against Your people” — in an 11th Century CE piyut (liturgical poem) recited on Mondays and Thursdays as part of Tachanun [supplication] (p.122ff). In addition, he outlines the “complete law-court argument prayer” which Moses offers immediately after the Golden Calf incident, Exodus/Shemot 32:9-14:
Here is manifest an example of complete law-court argument prayer: an opening address (verse 11), a defense argument (verses 12a, 13), a plea (or petition) (verse 12b), and a divine response (indirect) (verse 14). But the threat of destruction is not ended. Although God relents of His plan (verse 14), He still requires further appeasement…(Exodus 32:30-35)
The second argument should be considered as a continuation of the first, although structurally each can stand alone. First of all, it pursues the same line of argumentation as does the first. Second, it provides the real conclusion to the story (that is God’s actual sentence and its execution [verses 33-35]). Third, Moses’ ultimatum, “erase me,” seems to be a direct response to God’s offer in verse 10 to make of Moses a great nation. Fourth, Moses’ recounting of the event, in Deuteronomy 9:26-29, blends the two arguments of the Exodus story into a single unit. Finally, both arguments are needed to save the people fully.
— Anson, p.10-11