What does Romans 9:6 mean?

Paul has expressed his broken heart over the fact that the majority of Jewish people had rejected Christ as the Messiah and the way to salvation. He has listed many of the privileges God has given to Israel as His chosen people.

Paul now begins to deal with an enormous question, one that will dominate the next three chapters of Romans. If God gave to Israel all of those covenants and promises and privileges, what happens to His relationship with Israel now that they have rejected His Son?

Paul's first answer here is to defend the character of God. His Word has not failed. He will still keep His promises to Israel. God does not go back on His word. Then Paul begins to make a distinction between the physical descendants of Israel and what we might call "true Israel." He says something similar to what he wrote at the beginning of this letter in Romans 2:28–29: "For no one is a Jew who is merely one outwardly, nor is circumcision outward and physical. But a Jew is one inwardly, and circumcision is a matter of the heart, by the Spirit, not by the letter…"

Here Paul puts it more simply in saying that not everyone who is descended from Israel, ethnically, belongs to "true Israel." This matches similar statements made by Jesus during His earthly ministry (John 8:36–39).