In the time of Jesus, there was a prominent belief among the Jews that they would be “saved” expressly because they were Jewish. The Jews “inherited” salvation through Abraham. The New Testament has a running theme of countering this belief. The first ministry which the New Testament details is that of John the Baptist. His apocalyptic ministry was designed to convince the Jews to repent. As such, he had to counter this patriarchal, inherited salvation very early in his message:

Mat 3:8 Therefore bear fruits worthy of repentance,
Mat 3:9 and do not think to say to yourselves, ‘We have Abraham as our father.’ For I say to you that God is able to raise up children to Abraham from these stones.

Paralleled in Luke:

Luk 3:8 Therefore bear fruits worthy of repentance, and do not begin to say to yourselves, ‘We have Abraham as our father.’ For I say to you that God is able to raise up children to Abraham from these stones.

John’s point is very specific. The Jews believed that if God were to cut off Israel then God would be violating God’s promise to Israel. John counters this claim. John tells them to repent (the Jews were under the impression no repentance was necessary). John then explains how God could keep God’s promise to the Jews if they did not repent: by raising up new children of Abraham. John is countering the specific Jewish cliché that all Jews are saved by virtue of being Jewish.

Jesus also encounters this mentality:

Joh 8:33 They answered Him, “We are Abraham’s descendants, and have never been in bondage to anyone. How can You say, ‘You will be made free’?”
Joh 8:34 Jesus answered them, “Most assuredly, I say to you, whoever commits sin is a slave of sin.
Joh 8:35 And a slave does not abide in the house forever, but a son abides forever.
Joh 8:36 Therefore if the Son makes you free, you shall be free indeed.
Joh 8:37 “I know that you are Abraham’s descendants, but you seek to kill Me, because My word has no place in you.
Joh 8:38 I speak what I have seen with My Father, and you do what you have seen with your father.”
Joh 8:39 They answered and said to Him, “Abraham is our father.” Jesus said to them, “If you were Abraham’s children, you would do the works of Abraham.
Joh 8:40 But now you seek to kill Me, a Man who has told you the truth which I heard from God. Abraham did not do this.
Joh 8:41 You do the deeds of your father.”…

The claim was that due to being Abraham’s descendants that the Jews were not in bondage to sin. The Jews understood themselves as being saved apart from being righteous. Jesus tells them to repent, not to sin, and that they are not true children of Abraham (but of sin). Jesus is attacking inherited salvation by trying to sever the mental link between his listeners and Abraham’s lineage. Jesus’ point is that being descended from Abraham in no way guarantees salvation.

After Jesus’ death, this cliché was still alive and well. The letters in the New Testament attest to this fact. This might be hard for modern readers to understand, being separated by thousands of years after the culture in which these letters were written. But the letters consistently counter the claim that Jews are saved through Abraham apart from works.

The New Testament is written primarily in the form of letters. When the apostles were writing their letters they were not building sermonettes. The letters of the New Testament primarily are written to correct problems in the fledgling church. There is little moralizing and musing. The letters were written to address real issues. As such, when reading the letters of the New Testament the modern reader must realize they are reading one side of a conversation. The reader must put themselves in the mindset of piecing together the second half of the conversation.

The letter of James, most likely written very early, begins with countering this Jewish claim:

Jas 1:13 Let no one say when he is tempted, “I am tempted by God”; for God cannot be tempted by evil, nor does He Himself tempt anyone.
Jas 1:14 But each one is tempted when he is drawn away by his own desires and enticed.
Jas 1:15 Then, when desire has conceived, it gives birth to sin; and sin, when it is full-grown, brings forth death.
Jas 1:16 Do not be deceived, my beloved brethren.

Jewish Christians were claiming that their sin amplified God’s glory. God was using their sin to prove his righteousness in saving the Jews. James counters this idea. James says that God does not cause people to sin. God is in no way connected to sin.

James continued to counter this workless salvation throughout his letter:

Jas 2:14 What does it profit, my brethren, if someone says he has faith but does not have works? Can faith save him?

And:

Jas 2:17 Thus also faith by itself, if it does not have works, is dead.
Jas 2:18 But someone will say, “You have faith, and I have works.” Show me your faith without your works, and I will show you my faith by my works.
Jas 2:19 You believe that there is one God. You do well. Even the demons believe—and tremble!
Jas 2:20 But do you want to know, O foolish man, that faith without works is dead?
Jas 2:21 Was not Abraham our father justified by works when he offered Isaac his son on the altar?

James’ argument is that the Jews must show works in order to be saved. Faith alone will not save them, as they claim. James uses for illustration both demons and Abraham. The choice of Abraham is particularly fitting for James’ point. The Jews were saying they were saved by virtue of being descended from Abraham. James says “no, even Abraham was saved by works.”

Paul encounters this cliché as well. In Romans, Paul is writing his only letter to a church he did not himself found. As such, Paul is writing to a Jewish church filled with mostly Jewish Christians. This is why Romans is heavily centered on Jewish themes. In the second chapter, Paul introduces his counter-argument to the Jewish claim of inherited salvation by outright stating that only the doers of the law are justified:

Rom 2:13 (for not the hearers of the law are just in the sight of God, but the doers of the law will be justified;

Paul follows this up by exposing Jewish sin:

Rom 2:17 Indeed you are called a Jew, and rest on the law, and make your boast in God,
Rom 2:18 and know His will, and approve the things that are excellent, being instructed out of the law,
Rom 2:19 and are confident that you yourself are a guide to the blind, a light to those who are in darkness,
Rom 2:20 an instructor of the foolish, a teacher of babes, having the form of knowledge and truth in the law.
Rom 2:21 You, therefore, who teach another, do you not teach yourself? You who preach that a man should not steal, do you steal?
Rom 2:22 You who say, “Do not commit adultery,” do you commit adultery? You who abhor idols, do you rob temples?
Rom 2:23 You who make your boast in the law, do you dishonor God through breaking the law?
Rom 2:24 For “THE NAME OF GOD IS BLASPHEMED AMONG THE GENTILES BECAUSE OF YOU,” as it is written.
Rom 2:25 For circumcision is indeed profitable if you keep the law; but if you are a breaker of the law, your circumcision has become uncircumcision.

Notice Paul’s points. The Jews were boasting in God. The Jews were proselyting the Gentiles to be righteous. The Jews were sinning themselves. The Gentiles knew the Jews were sinners. And the Jews still believed they were saved (thus Paul must state that their circumcision is made uncircumcision).

Paul attacks the heart of the Jewish claim in the next section:

Rom 3:5 But if our unrighteousness demonstrates the righteousness of God, what shall we say? Is God unjust who inflicts wrath? (I speak as a man.)
Rom 3:6 Certainly not! For then how will God judge the world?
Rom 3:7 For if the truth of God has increased through my lie to His glory, why am I also still judged as a sinner?
Rom 3:8 And why not say, “Let us do evil that good may come”?—as we are slanderously reported and as some affirm that we say. Their condemnation is just.

In verse 5, Paul is quoting the Jewish argument. The Jews were claiming as a mechanism for inherited salvation that the worse of a sinner that God saved, the more it would show God’s righteousness. This echoes the letter of James in which Jewish Christians were claiming their sin was from God.

Paul counters this by claiming that under this standard that God could not judge the world. God would be unfair not to save the lost Gentiles if God were to save the unrighteous Jews. Paul takes this opportunity to address false rumors about Paul’s own ministry. Paul was preaching salvation apart from the law, and the same accusation about inspiring lawlessness were leveled against Paul as were the Jews who believed in inherited salvation.

Paul continues on, countering this Jewish claim:

Rom 3:23 for all have sinned and fall short of the glory of God,

Paul points out that no man is safe and that boasting in the law is vain. Later on, Paul takes the same stance that Jesus used for countering inherited salvation:

Rom 9:3 For I could wish that I myself were accursed from Christ for my brethren, my countrymen according to the flesh,
…
Rom 9:6 But it is not that the word of God has taken no effect. For they are not all Israel who are of Israel,
Rom 9:7 nor are they all children because they are the seed of Abraham; but, “IN ISAAC YOUR SEED SHALL BE CALLED.”

Paul wishes himself dead to save all of Israel (something he knows is unrealistic). Paul’s point is that not all who are of Israel would be saved (contrary to popular belief). Paul then states that not all who are currently Israel are of Israel. Paul is saying the boarders of who are being saved extend wider than inheritance as even the pagans at the time noted. Cassius Dio records:

They have also another name that has been acquired,–i.e., the country has been called Judaea, and the people themselves Jews. I do not know from what source this title was first given them, but it applies also to all the rest of mankind, although of foreign race, who cherish their customs.

Paul then explains that although more than just Abraham’s descendants would be saved, that not all of Abraham’s descendants would be saved. Paul is creating a mental Venn diagram. Paul then explains how God’s promises do not apply to the parts of Israel which will be cut off. Paul illustrates:

Rom 9:7 nor are they all children because they are the seed of Abraham; but, “IN ISAAC YOUR SEED SHALL BE CALLED.”
Rom 9:8 That is, those who are the children of the flesh, these are not the children of God; but the children of the promise are counted as the seed.

Paul’s point is that not all of Abraham’s decedents are considered Israel. Abraham had two sons, Isaac and Ishmael. The decedents of Ishmael are not considered the seed of Abraham. Likewise, Isaac had two sons but only one is considered Israel:

Rom 9:9 For this is the word of promise: “AT THIS TIME I WILL COME AND SARAH SHALL HAVE A SON.”
Rom 9:10 And not only this, but when Rebecca also had conceived by one man, even by our father Isaac
Rom 9:11 (for the children not yet being born, nor having done any good or evil, that the purpose of God according to election might stand, not of works but of Him who calls),

Here is Paul’s point: not everyone who is descended from Abraham is saved. Likewise, those who are currently considered Jews should be under no impression that they too are saved expressly for being Jewish. Paul was countering this early Jewish cliché.

Throughout the New Testament, the text confronts and refutes the Jewish claim that salvation was of the Jews, that salvation was inherited and not earned. Jesus even states this common claim to flip it on its head:

Joh 4:22 You worship what you do not know; we know what we worship, for salvation is of the Jews.
Joh 4:23 But the hour is coming, and now is, when the true worshipers will worship the Father in spirit and truth; for the Father is seeking such to worship Him.

Here is the Biblical answer, salvation is of those who worship God.