We see the same principle reiterated in the book of James. In James 2:10-13 he writes:
10 "For whoever keeps the whole law and yet stumbles in one point, he has become guilty of all. 11 For He who said, "Do not commit adultery," also said, "Do not commit murder." Now if you do not commit adultery, but do commit murder, you have become a transgressor of the law. 12 So speak and so act as those who are to be judged by the law of liberty. 13 For judgment will be merciless to one who has shown no mercy; mercy triumphs over judgment."
Here we see that the abiding principle throughout the New Testament is that if you base your salvation on law, then you subject yourself to the demands of the law. The law demands that if you stumble in one point, then you are guilty of disobeying all, and thus you will be condemned with everyone else. Notice that James tells them to seek to be judged by the "law of liberty" where there is mercy, for it is only the God of mercy that can forgive transgressions. The Law can never forgive, for it was never designed to do so.
Incidentally, why do you think James speaks of the sin of "murder" in this context? The answer will reveal to us the nature of the New Covenant. The context begins from James 2:1 through 2:9. In it, James admonishes the Christians for showing favoritism to the rich man and despising the poor man. In doing so he says in verse 8 that they are ignoring the command to "love your neighbor as yourself," and thereby, he says in verse 9, that they are "committing sin." If we remember what Jesus taught in Matthew 5:21-23 that I mentioned earlier, we can see why James associates the sin of "murder" with despising the poor man. For in despising him, we have made a fool of him, and thereby we have spiritually murdered him. Thus we see how sensitive the New Covenant is. It is not merely interested in outward behavior, but the behavior of the heart.
Now back to the Law. Let's look at another passage which teaches the same principle (that the WHOLE law had to be set aside for grace to come).
Colossians 2:13-14 says:
13 "When you were dead in your transgressions and the uncircumcision of your flesh, He made you alive together with Him, having forgiven us all our transgressions, 14 having canceled out the certificate of debt consisting of decrees against us, which was hostile to us; and He has taken it out of the way, having nailed it to the cross."
Notice again that Paul is speaking to Gentiles, since he uses the phrase "the uncircumcision of your flesh." He tells them that there sins were forgiven by God "having canceled out the certificate of debt consisting of decrees against us." What does this "certificate of debt consisting of decrees" refer to? Well, it cannot refer to the Jewish ceremonial law, for that was never "against" the Gentiles. Rather, it refers to the whole Law found in the Old Covenant, the Law that was originally given to Adam and perpetuated through Israel until the time of Christ, where it was finally "nailed to the cross."
Paul teaches something similar in Ephesians 2:15, but with a little twist. He writes:
15 by abolishing in His flesh the enmity, which is the Law of commandments contained in ordinances, so that in Himself He might make the two into one new man, thus establishing peace, 16 and might reconcile them both in one body to God through the cross, by it having put to death the enmity.
Notice the precise phrasing "the Law of commandments contained in ordinances." The Greek is "to:n novmon tw:n ejntolw:n ejn dovgmasin," which literally means "the law of the commandments in decrees." This can be none other than the WHOLE law of the Old Covenant. In fact, the word "ordinances" (dovgmasin) is the same word used in Colossians 2:14 in the phrase "certificate of debt."
Now, the "twist" Paul adds to this is to say that the setting aside of the Old Covenant law resulted in making Jew and Gentile into one body. Here is one of those places where the "Jew/Gentile" theme appears right along side the "grace versus law" theme. We find that, just as Romans 3:9-20 said that the Gentiles were "under the law" and that "works of the law" could not justify either Jew of Gentile, so we find here in Ephesians 2:15 that the Gentiles were under the law and condemned. Again, this shows us that the Law must refer to the WHOLE law.
Paul teaches the same truth in 2 Corinthians 3:7-9:
7 But if the ministry of death, in letters engraved on stones, came with glory, so that the sons of Israel could not look intently at the face of Moses because of the glory of his face, fading as it was, 8 how will the ministry of the Spirit fail to be even more with glory? 9 For if the ministry of condemnation has glory, much more does the ministry of righteousness abound in glory.
"Works of the Law" - Page 16