First off we need to understand who Israel is as defined by the Bible...
Rom 9:4 Who are Israelites; to whom [pertaineth] the adoption, and the glory, and the covenants, and the giving of the law, and the service [of God], and the promises;
Rom 9:5 Whose [are] the fathers, and of whom as concerning the flesh Christ [came], who is over all, God blessed for ever. Amen.
Rom 9:6 Not as though the word of God hath taken none effect. For they [are] not all Israel, which are of Israel:
Rom 9:7 Neither, because they are the seed of Abraham, [are they] all children: but, In Isaac shall thy seed be called.
Rom 9:8 That is, They which are the children of the flesh, these [are] not the children of God: but the children of the promise are counted for the seed.
Rom 9:9 For this [is] the word of promise, At this time will I come, and Sarah shall have a son.
What does the scripture mean when it says they are not all Israel which are are of Israel? The passage suggests that the concept behind Israel has more than physical and hereditary implications... It means you could still be a Jew, but not be a part of the true Israel. The Bible speaks of an Israel of God and an Israel according to the flesh(1 Corinthians 10:18) Who are the children of promise and Abraham's seed?
Gal 3:26 For ye are all the children of God by faith in Christ Jesus.
Gal 3:27 For as many of you as have been baptized into Christ have put on Christ.
Gal 3:28 There is neither Jew nor Greek, there is neither bond nor free, there is neither male nor female: for ye are all one in Christ Jesus.
Gal 3:29 And if ye [be] Christ's, then are ye Abraham's seed, and heirs according to the promise.
Its plain that Israel according to the flesh are not the children of God and the true seed of Abraham are those in Christ. If you read the following passage carefully the answer is found within in regards who the Israel of God is.
Gal 6:15 For in Christ Jesus neither circumcision availeth any thing, nor uncircumcision, but a new creature.
Gal 6:16 And as many as walk according to this rule, peace [be] on them, and mercy, and upon the Israel of God.
Its obvious that the Israel of God, or true Israel are Christians. Paul said that being of the circumcision(the jews) and uncircumcision(gentiles) means nothing, but all that matters is being a new creation( in Christ). He also says that there is no difference between greek or jew. Therefore by logical deduction the Israel of God must be Christians, because If the Israel of God were hereditary Israel or even believing Israelite's then Paul would be contradicting himself in what he just said in the passage prior. The passage of scripture preceding the Israel of God mention states there is no difference or superiority between jew or greek in Christ so to assume Paul was referring to the Israel of God as believing jews or hereditary jews would not make sense, because it sets up a special recognition or idea of a class within a class that Paul just discredited.