All we need do to show that Luther's "by faith alone" is not the whole biblical picture is cite James 2:24: "so we see that a person is justified by works and not by faith alone." Paul himself never uses the adverb "alone" when speaking of justification by faith. The closest he comes is in Romans 3:28 when he says, "a person is justified by faith and not by works of law."
As we might expect, the meaning of faith and its relationship to deeds in Paul is somewhat complex. We might summarize the landscape as follows:
1. We should not understand faith and works to be mutually exclusive concepts. In 1 Thess. 1:3, Paul commends the Thessalonians for their "work of faith." Also, faith by its very nature "works," as in Gal. 5:6, where Paul says that neither circumcision nor uncircumcision matters--only faith working through love. Eph. 2:8-10 can say from one verse to the next that we are saved by grace through faith, not of works, and then say in the next verse that we were created for good works--clearly the two concepts do not contradict each other.
2. Paul does teach that a person cannot merit justification by his or her works--no amount of deeds merits a "not-guilty" verdict. However, since Augustine we are prone to see this as an abstract faith versus works proposition. Paul surely processed the expression "works of law" by way of the Jewish law. And since Paul's primary topic of discussion is the differences between Jew and Gentile, arguing that Jews do not have a different path to justification than Gentiles do, we should primarily think of the phrase "works of law" as a reference to law observances that distinguished Jew from Gentile (circumcision, sabbath observance, food laws, etc...). Paul's point is thus that a Jew did not stand a better chance at justification simply because they were Jews. All have sinned--both Jew and Gentile. All need the faithful death of Jesus Christ in order that their sins might be atoned for and they might be redeemed.
3. The expression "through the faith of Jesus Christ" in Romans 3:22a and Galatians 2:16a is likely a reference to the faithfulness (to death) of Jesus, his obedience unto death. In that sense, the most important faith by which we are justified is not even our own. "I have been crucified with Christ and I no longer live, but Christ lives in me. And what I now live in the flesh, I live by trust/in the faith of the Son of God who loved me and gave himself for me" (Gal. 2:20). The word order suggests to me that Paul wants the audience to hear both connotations. First they hear, "in faith I live" and think of their own faith. Then Paul tacks on "the of the Son of God [faith]" and they think of his faithfulness unto death.
4. But Paul does move the train of thought in both Romans 3 and Galatians 3 to human faith as the principle for our justification. Romans 4 uses the example of Abraham's faith in the God who justifies the ungodly (4:5) and who raises the dead (4:17, 24) as a model for our justification.
The point of justification by faith in Christ versus works of law is thus not that works of law are bad. In fact, we would argue that for a Jew they remain important as part of their ongoing relationship with God. Paul never encourages Jews to stop observing the Jewish law in its ethnic particulars. Only when purity regulations came into conflict with more essential principles like the unity of the body of Christ did Paul "fudge" on aspects of the Jewish law (Gal. 2:11-14)
They simply are inadequate to justify. In fact, Paul explicitly denies that we make void law because of faith (3:31). Faith thus does not even remove the principle of law!
5. While works are not adequate to justify a person, faith expresses itself through appropriate works. On the Day of Judgment, God "will repay to each according to his works" (Rom. 2:6). On that day, "to those who from strife and who disobey the truth and to those persuaded by unrighteousness, wrath and anger..." (2:8). "It is necessary for us all to appear before the judgment seat of the Messiah so that each might receive the things [appropriate] to the things which s/he practiced in the body, whether good or bad" (2 Cor. 5:10).
Indeed, far from faith removing works as a basis for judgment and "final" justification, faith brings the Spirit which enables the works necessary for justification. "Do we cancel law therefore through faith? God forbid! But we establish law" (Rom. 3:31). "Shall we continue in sin that grace may abound? God forbid! How will we who have died to sin still live in it?" (6:1-2). And of course Paul speaks of Gentiles who "demonstrate the work of the law written on their hearts" in Rom. 2:15. These individuals "by nature do the things of the law" (2:14). This language is reminiscent of Jer. 31 cited in Hebrews 8, 10 and alluded to in 2 Corinthians 3. It is new covenant language that pushes us to see these Gentiles as individuals who have the Spirit and are thus able to fulfill the righteous expectation of the law (Rom. 2:26; 8:4).
The confusing part of Paul's rhetoric is that he almost functions with two different conceptions of law here. Works of law have overtones of Jewish particularism and ethnic boundary issues. But in Romans 2 and 8, law seems to refer to a certain kind of core law that a Gentile might keep by nature even though uncircumcised. For our discussion, the important thing to notice is that Paul claims that the person who is unable to keep the law in Romans 7 is able to do so in Romans 6 and 8. And while works cannot justify in themselves, they are necessary for final justification in his thought.
Clearly Paul's thinking here is problematic for Lutheran theology in particular. On this point especially, Wesleyan-Arminian theology is beautifully situated between Roman Catholicism and Lutheranism in relation to Paul's thought. If medieval Catholicism did not have an appropriate sense in which grace asks for faith as its initiator, Lutheranism did not have an appropriate sense of how grace asks for particular works--here understood as the avoidance of sin rather than good deeds--as essential for final justification. Wesleyan-Arminian theology correctly holds to both: faith as the only effective solicitation of God's grace and works as a natural (and essential) by product of faith brought through the Spirit, where works are here understood more as the avoidance of sin rather than positive good deeds.