For the previous crumb, see here. This post begins chapter two, "How Salvation Works"
The Bottom Line
One of the biggest secrets in human relationships is to recognize that the arguments and words coming out of someone's mouth may not actually be the primary, underlying issue, what really has the person charged up. They may not even realize it. Sometimes you have to dig a little deeper to get down to what is really bothering them or what really has them upset. The person who responds in such cases on a purely logical level, only engaging his or her words, may in fact be completely missing what is really going on.
In a somewhat similar vein, E. P. Sanders suggested that Paul's argument developed "from solution to problem."  Sanders' interpretation went a little like the following. Paul knew that God had chosen Jesus as the way to reconcile Israel to himself. And if Jesus was the way, then the Jewish Law was not the way. And if the Jewish Law was not the way and the cross was the way, then non-Jews, Gentiles, could be reconciled to God just as easily as Jews could.
We do not have to accept Sanders' entire perspective to see how God might have unfolded Paul's understanding. Paul had kept the Jewish Law brilliantly as a Pharisee. If anyone was right with God, he might have thought, surely I am. But then he witnessed the risen Jesus, which implied that his Law-keeping was not sufficient, was not the way God had chosen. Rather, the cross of Jesus was the way God was reconciling Israel to himself. Sanders put it rather bluntly--the problem with the Law was that it was not Jesus.**
If one of the primary purposes of the Jewish Law for Paul the Pharisee was as a fence to guard the Jews against the nations, then the cross would have even more radical implications for Paul.  In keeping with Jesus' own agenda of including the discarded of Israel, God revealed to Paul that the inclusion must go much further than Israel. If the cross trumped the Law as the way to reconciliation, then potentially even Gentiles could be included through the cross. Passages like Isaiah 11 must have jumped out at him, a passage he understood as a prophecy that the Gentiles would hope on the Jewish messiah (cf. Rom. 15:12).
The bottom line for Paul was thus that Gentiles could now be right with God through the cross of Jesus, as well as that the Jewish Law could not make you right with God. The arguments of Romans and Galatians basically play out these fundamental understandings. The idea that the Jews themselves relied on God's grace for a right standing with Him was already something Jews acknowledged.  All Jews would have agreed with Paul that they had sinned at some point in their lives and that Israel's good standing with God was a matter of His grace.
But non-believing Jews did not agree that the death of Jesus was a sacrifice to atone for the sins of Israel. And the believing Jews in Jerusalem did not agree that Jewish believers were any less obligated to keep the Jewish Law than they were before. These are the underlying positions that Paul sets out to defend in the argument of Romans.
 In the first volume of this two part series, Paul: Messenger of Grace, we had a running series in the endnotes of the thirty or so books on Paul that a person might read to become a Paul expert. One of the key books on that list was E. P. Sanders' landmark book, Paul and Palestinian Judaism (**, 1977). Perhaps we should add to that list another of Sanders' books, Paul, the Law, and the Jewish People (**).
 A famous line in an early second century Jewish book in Greek called the Letter of Aristeas says that, "***"
 This is one of the key insights of the "new perspective" on Paul and Judaism that has developed over the last thirty years. Judaism never thought that a person could "earn" a right standing with God. And as Sanders pointed out in Paul, the Law, and the Jewish People (**), keeping the Jewish Law was not about "getting in" to Israel or the people of God. It was about "staying in" in the people of God.
It is perhaps understandable that Lutheran and Calvinist interpreters of Judaism would equate its emphasis on works as a sign of works-righteousness. It thus took a Methodist (Sanders) to recognize that the Jewish Law-keeping was much more in response to God's grace toward and covenant with Israel than it was an attempt to earn a righteous status.