Written in 2010.
We will consider two passages in Romans which shed light on the question.
6 But it is not as though the word of God has failed. For not all who are descended from Israel belong to Israel, 7 and not all are children of Abraham because they are his offspring, but "Through Isaac shall your offspring be named." 8 This means that it is not the children of the flesh who are the children of God, but the children of the promise are counted as offspring. (Rom. 9:6-8 ESV)
The first critical sentence is 'For not all who are descended from Israel belong to Israel', in which it is clear that there are two distinct senses of the word Israel in this verse. The context of v6 is that, in view of the Jewish rejection of Christ, it may appear that the word of God has failed. Paul refutes that in v6 by distinguishing national Israel from a different, greater Israel. The phrase 'descended from Israel' seems to denote national Israel. To support this, note that this sentence is in parallel with the first half of v7 'not all are children of Abraham because they are his offspring [Gk. seed]'. Thus, being an offspring or descendant of Abraham is put in parallel with descended from Israel.
If not everyone descended from Israel belongs to Israel, then it is clear that the latter is a distinct entity, yet also called Israel. Note that if not all who are descended from Israel belong to this other entity called Israel, it follows that some do belong to it. In other words, some of those who are descended from Abraham (national Israel) do belong to the Israel in the latter sense.
So what is this entity called Israel which is not national Israel, composed of Abraham's offspring? It follows directly that not all members of this Israel are Jews; hence, this Israel contains Gentiles. Therefore, this Israel is not national Israel, although it contains members of national Israel, and is greater than national Israel, since it contains Gentiles.
In v8 the children of the flesh are used to describe children of Abraham who are not through Isaac; the children of the promise are Abraham's offspring through Isaac, and it is these who are called the children of God. The contrast of v8 parallels the contrast in v7, which implies that the physical offspring of Abraham (national Israel) is put in contrast with the children of the promise which are through Isaac. If the children of the flesh are correlated with national Israel, then the children of the promise are correlated with the greater Israel, the second sense of the word.
The objection that national Israel is through Isaac and, hence, the children of the promise refers to the national Israel destroys the flow of the text and invalidates the contrasts being made, particularly in v7. No, the children of the promise come through Isaac, and this is something distinct and greater than the physical offspring of Abraham.
25 Lest you be wise in your own sight, I do not want you to be unaware of this mystery, brothers: a partial hardening has come upon Israel, until the fullness of the Gentiles has come in. 26 And in this way all Israel will be saved, as it is written, "The Deliverer will come from Zion, he will banish ungodliness from Jacob"; 27 "and this will be my covenant with them when I take away their sins." (Rom. 11:25-27 ESV)
The context of the passage is Paul’s preceding explication of the Gentiles as branches having been grafted onto the Jewish tree of God’s people. Paul is warning the Gentiles against conceit. The critical question to ask is what are the Israel of v25 and of v26. In v25, Israel is contrasted with the Gentiles, and this suggests that the Israel of v25 refers to national Israel. This is also consistent with its preceding context of contrasting the Jews and Gentiles as members of God’s tree.
To determine the reference to Israel in v26, we ask what does 'in this way' in v26 refer to? It refers to the fullness of the Gentiles coming in. Therefore, by the fullness of the Gentiles coming in, all Israel will be saved. This implies that the fullness of the Gentiles coming in completes Israel, thus, Israel in v26 cannot refer to national Israel. So the sense of Israel in v26 is not that of national Israel in v25 and preceding. As in the Romans 9 passage, here it is also clear that there is an entity of Israel which is distinct from national Israel and greater than national Israel, since it contains the Gentiles.
Yet 'until the fullness of the Gentiles has come in' suggests that the state of hardness of national Israel will also be changed once the Gentiles have come in. Such a view would lead to an expectation that Jews will, as a people, return to the Lord once the Gentiles have come in. v27-32 do not preclude that possibility, as far as I can see. Yet it's not clear if this understanding is generally supported by other NT passages, or if it is required by the Romans passages under consideration.
There is a distinct sense that, going back to the patriarch Abraham, something greater than physical offspring are in view. Abraham will have offspring by some means, as it were, other than the flesh, and this is the true intent and purpose of his life. Yet, his physical offspring are a picture or representation of the greater reality, one not readily visible.