One of the points more commonly made in the discussion on the interpretation of Paul's letters and doctrine of justification is this: keeping the Law was not and continues not to be the kind of burdensome, impossible task that the traditional understanding makes it out to be. Insofar as the traditional interpretation of Paul presupposes this, we consequently are confronted with one of two problems: either Paul's doctrine is critically compromised and mistaken vis-a-vis the Law; or else we have poorly misunderstood Paul.
Certainly one of the stronger points to be made in favor of this anti-traditionalist argument is that much of Judaism at the time of Paul did not consider the Law to be so profoundly impossible or burdensome. You need only to read the 119th psalm, for instance, to find dozens of statements to the effect that the author has kept the law, has decided to keep the law, or that God should assist him insofar as he is righteous, etc. Another regular motive of the psalms (and not only the psalms!) is the distinction of the world into the righteous and the unrighteous, neither of which category is affirmed to be universal or empty. There are the righteous, and there are the sinners.
In fact, even many of the texts Paul cites in Rom 3.9ff., when making the case that "no one is righteous," nevertheless affirm that there are some righteous persons. Ps 14 affirms that God is with the company of the righteous (v. 5), clearly meaning Israel whereas the unrighteous previously mentioned are of the nations. The author of Ps 5 lauds himself as one who takes refuge in the LORD (v. 11) and one of the righteous whom God blesses and shields (v. 12), in contradistinction to the unrighteous whose throats are open graves (v. 9).
What can be said in favor of the traditionalist view, then?
It seems to me nevertheless inevitable that Christ came to fulfill the Law and the Prophets (Mt 5.17), that none of his opponents kept the Law (John 7.19), that the Law was a burden the Jewish disciples themselves could not bear (Acts 15.10). The coming of Christ as fulfillment of the Law, and as a death for our sins (1 Cor 15.3), to my mind presupposes the inability of human persons adequately to keep the Law and to sacrifice appropriately for their sins. In other words, Christ reveals something that ancient Judaism, whether of the first century or previous to that, simply did not understand.
Stephen Westerholm, Justification Reconsidered: Rethinking a Pauline Theme (Eerdmans, 2013) says the following:
Why did Paul think so differently from other Jews [regarding human sinfulness and inability]? We can only speculate, of course, but a natural reason suggests itself. As long as one believes that (whatever is to be said of Gentiles) Jews will be "saved" provided they show a basic willingness to comply with the laws of the covenant (some Jews set the standard higher than that; but some did not), one will naturally believe them capable of showing at least the required modicum of obedience. So Paul himself presumably believed prior to his life-changing trip to Damascus. But once he was convinced that Jesus was, after all, God's Messiah, then Christ's crucifixion, far from discrediting messianic claims on his behalf, had to find a place in the divine plan for messianic redemption. It follows that humanity's predicament must be more desperate than Jews otherwise imagined. Human beings must not, after all, be capable of the modicum of obedience required by the covenant (p. 33).
Christ's cross, then, tells us that the obedience God demands is higher than we can imagine, and the punishment for sin is stricter than we might have thought. We have to allow God's revelation in Christ to form our thinking in this matter; there is no guarantee or even slight reason to think that 1C Judaism was right about the human predicament and Paul must have been horribly mistaken.