Abraham's Covenant Children

I think yo-mama has, in the last comment thread, given me a very good place to pick up:

To shed light on the question, I'd ask another question: to what degree were children of believers in the old covenant to be treated as members and participants in the covenant of God? Then, how has this changed (if at all) in the new testament? The answer to the first is simple--to the highest possible degree. This may be helpful since things were more explicit in these regards in the OT.

Some observations from the Pentateuch to put some meat to her very helpful comment:

When God established his covenant with Abraham in Gen 17, He was also explicitly making this covenant with Abraham's children throughout their generations forever. These children were, therefore, by their very birth, to be considered within the bounds of that covenant, and all the males were automatically to receive circumcision as the sign thereof. We read in Gen 18 that this arrangement carried with it the obligation upon Abraham to "command his children and his household after him to keep the way of the LORD by doing righteousness and justice"

From the day that children were born into these covenant households, then, they had claim on the promises of the covenant (that God would give them a land) and were bound by the duties (to keep the LORD's ways). Their fathers had the responsibility to command them in these ways. Again, none of this was dependent upon anything other than their being born into Abraham's family. This same arrangement is established to each of the patriarchs in turn (Gen 26).

It seems to me that in this foundational example, we see the essential elements of what it means to be in covenant with God. When I say that someone is in covenant with God, I mean that they are 1) rightful claimants of the promises given and 2) proper subjects of the duties proscribed. Again, this was presumed to be true of Abraham's descendants as soon as they were born.

These same principles hold true through the rest of the Torah. God's covenant with his people developed and new promises and new duties were revealed, promises and duties connected with the Passover (Ex 12), with the priesthood (Ex 30) and certainly with Israel's stay at Sinai (Ex. 20), all of which were automatically to be passed on from father to son. Moses reiterated these truths as Israel was preparing to enter the promised land (Deut 6).

So, to what degree were children of believers in the Old Covenant to be treated as members and participants in the covenant of God? Yo-mama's answer appears quite consistent with what I've been able to find in the Pentateuch: to the highest possible degree. Each child born into an Israelite household was-from his very birth- presumed to be 1) entitled to inheritance of all the promises and 1) obligated to performance of all the duties of that covenant.

I want to press on through the Psalms and prophets before considering to what extent (if any) this arrangement has been altered with respect to the New Covenant. I'd also like first to consider Rev's question about the status of those leaving the covenant from the perspective of the entire OT. The phrase "cut off from his people" is the only thing that comes to mind so far.