I believe the people of God consists in scriptural language of all Jews and Gentiles, meaning all people who put their faith in Jesus as Lord, Savior and Messiah/Christ.
After the setting of Genesis 1-11 in creation, fall, judgment and redemptive promise and further judgment, we read of the call of God to Abraham and God's promise that in Abraham and in his seed all peoples on earth would be blessed.
Paul argues from this scripture that the seed refers to one person, Christ. Its fulfillment extended beyond the Old Covenant to the New Covenant in which there is one holy nation scattered throughout the earth, the people of God.
Today there are popular television preachers and books they write which insist that ethnic Jews are the people of God. I'm not saying they deny that we in Jesus are as well, but evidently they see two sets of people as being "the people of God." To insist in this is to insist that the Old Covenant is still in effect. But we know that in Jesus Christ the New Covenant has come, and that therefore the Old Covenant is a thing of the past.
This same problem occurs related to the above, when these books and people insist that Israel has a right to all the land promised by God in the Old Covenant. On what ground? On the ground of the Old Covenant. But in Christ Jesus, in the New Covenant, the whole earth is promised to the people of God. This is what is in effect today; the Old Covenant is no longer.
The Old Covenant is still important for us as the starting point and basis for the New Covenant that God has effected in Christ, in the Story of God. And I believe that God is at work among the ethnic Jews and has not forgotten them, as Paul clearly says. But let's not make the mistake of thinking that ethnic Jews apart from faith in Jesus as Messiah have any claims on God's promises. Nor let us assume that the promises of the Old Covenant as they were given, are still in effect today. They must be read through the lens and promises of the New Covenant in Jesus. They are fulfilled in the New Covenant in Jesus.
What might you disagree with on this and why? Does this interpretation of scripture deny that God is at work in the world, including what is happening today in the Middle East? (I hope not!)