I think the problem is that many people either look to the law completely or use not being subject to the law as an excuse to living however they want. These are two extremes. Paul referred to the law as a "schoolmaster" to bring us to Christ. Based on contextual readings of other writings of Paul it is clear that Paul is not dismissing the law. The law is important. The point is that no one is good enough on their own merit to fully keep the law and live a perfect and sinless life (except Christ, who is God made flesh). This is why the law is a schoolmaster to bring us to Christ. In Galatians 3:10 what he is saying is that if we are depending on our keeping of the law to save us we are cursed, because we can't keep it perfectly. In Romans 8: 2-7 Paul says:
"For the law of the Spirit of life in Christ Jesus hath made me free from the law of sin and death. For what the law could not do, in that it was weak through the flesh, God sending his own Son in the likeness of sinful flesh, and for sin, condemned sin in the flesh: That the righteousness of the law might be fulfilled in us, who walk not after the flesh, but after the Spirit. For they that are after the flesh do mind the things of the flesh; but they that are after the Spirit the things of the Spirit. For to be carnally minded is death; but to be spiritually minded is life and peace. Because the carnal mind is enmity against God: for it is not subject to the law of God, neither indeed can be."
What he is saying here is that the law is not enough. We need grace. That is not to say that grace gives us a license to ignore God's law, though. In Romans 5:20-6:2 Paul said:
"Moreover the law entered, that the offence might abound. But where sin abounded, grace did much more abound: That as sin hath reigned unto death, even so might grace reign through righteousness unto eternal life by Jesus Christ our Lord. What shall we say then? Shall we continue in sin, that grace may abound? God forbid. How shall we, that are dead to sin, live any longer therein?"
In other words, if we accept God's grace we won't want to follow after sin. That is not to say that we will be perfect, but our imperfection will be made perfection through the grace of God who will give us the desire to live lives that are pleasing to Him. James said in James 2: 15-20:
"If a brother or sister be naked, and destitute of daily food, And one of you say unto them, Depart in peace, be ye warmed and filled; notwithstanding ye give them not those things which are needful to the body; what doth it profit? Even so faith, if it hath not works, is dead, being alone. Yea, a man may say, Thou hast faith, and I have works: shew me thy faith without thy works, and I will shew thee my faith by my works. Thou believest that there is one God; thou doest well: the devils also believe, and tremble. But wilt thou know, O vain man, that faith without works is dead?"
What James is saying here is not that good works saves us, but that is shows our faith. If we say we have placed our faith in Jesus but don't live lives pleasing to Him we are not demonstrating our faith. This is not to say that we will lose our salvation if we don't keep doing good works. Ephesians 2: 8-9 makes it clear:
"For by grace are ye saved through faith; and that not of yourselves: it is the gift of God: Not of works, lest any man should boast. For we are his workmanship, created in Christ Jesus unto good works, which God hath before ordained that we should walk in them."
In other words, we are saved by faith. Works have nothing to do with salvation. They are, however, important in that they are an outward manifestation of our faith. As Jesus said in Matthew chapter 7: 16-20.
"Ye shall know them by their fruits. Do men gather grapes of thorns, or figs of thistles? Even so every good tree bringeth forth good fruit; but a corrupt tree bringeth forth evil fruit. A good tree cannot bring forth evil fruit, neither can a corrupt tree bring forth good fruit. Every tree that bringeth not forth good fruit is hewn down, and cast into the fire. Wherefore by their fruits ye shall know them."
Our works are a manifestation of our faith. The truth is that there are many different perspectives among NPP scholars, and it would probably be more accurate to use the plural form "New Perspectives on Paul." As is often the case, there are about as many perspectives out there as there are scholars. Since many see faith and works as both having importance it is likely that there are some who would agree with my statements above, and some that would disagree. NPP scholar N.T. Wright stated "There are probably almost as many 'new' perspective positions as there are writers espousing it – and I disagree with most of them."
One prominent theologian among the NPP is E.P Sanders. In "Paul and Palestinian Judaism" Sanders said that the Jewish people of the first century taught that they were the people of God by virtue of God's covenant with Abraham, and stayed in it by keeping the Law. Paul believed that the only way to become one of the People of God was through faith in Christ and the Old Covenant was no longer sufficient. But, once inside, appropriate behavior was required of the Christian, behavior based on the Jewish Scriptures, but not embracing all aspects of it. Both patterns required the grace of God for election (admission), and the behavior of the individual, supported by God's grace. The dividing line, therefore, was Paul's insistence on faith in Christ as the only way to election. However, Sanders stressed that Paul also “loved good deeds” and that when his words are taken in context, it emerges that Paul advocates good works in addition to faith in Christ.
It seems, then, that Sanders at least would see Galatians 3:10 as an indication that the covenant law of the Old Testament is not enough for election and that dependence on following the law in an attempt to earn one's salvation will result in one being cursed. At least that is my understanding of what Sanders was saying in his writings.