Paul is clear: our acceptance with God isn't by being religiously sincere or by being faithful or by having faith in general or even by having faith in God. It is by faith in Christ Jesus.
The phrase translated "faith in Jesus Christ for all those who believe" (Rom. 3:22) has stirred considerable discussion. Note the parallel text in Gal. 2:16:
"Nevertheless knowing that a man is not justified by the works of the Law but through faith in Christ Jesus, even we have believed in Christ Jesus, that we may be justified by faith in Christ, and not by the works of the Law; since by the works of the Law shall no flesh be justified."
The two phrases in italics could be translated literally, faith of Christ Jesus. Most translate them as faith in Christ, thus a reference to our faith in the Son of God, our trusting of him to save us from sin. On this view, Jesus is the object of our faith.
More recently numerous scholars have argued that this is a reference not to our faith in Christ but to the faithfulness of Jesus himself. If so, Paul's point would be that because Jesus was faithful, because his life was a perfect demonstration of faithful obedience to his heavenly Father, we have a basis for our acceptance with God. We put our faith in the faith(fulness) of Jesus and are thereby justified.
Theologians have called this the Active Obedience of Christ, his sufferings on the cross being his Passive Obedience (cf. Rom. 5:19).
Paul uses the phrase "faith of Jesus Christ" seven times in his epistles: Gal. 2:16(2); Gal. 3:22; Rom. 3:22,26; Eph. 3:12; Phil. 3:9. Each of these texts would make sense if we translated them as referring to the faithfulness of Jesus himself. Cf. also the "faithfulness of God" (Rom. 3:3) and the "faith of Abraham" (Rom. 4:16). If interpreted this way, this would not diminish the importance of our faith in Christ. Indeed, see Rom. 3:22 ("for all those who believe"); Gal. 2:16; 3:22; Phil. 3:9.
If Paul is thinking of the faithfulness of Jesus as the foundation or basis of our acceptance with God, then justification may, in a sense, be conceived as being both by works and by faith. That is to say, we are justified by faith in the works of Jesus.
Still, it must be noted that much can be said for the traditional interpretation that our faith in Christ is Paul's intent. Tom Schreiner (Romans, Baker Exegetical Commentary) appeals to four arguments:
First, "both Romans and Galatians have a plethora of passages that refer to the faith of believers" (185; he cites 38 such texts).
Second, "nowhere is there any unambiguous indication that Paul spoke of the faith/faithfulness of Christ. . . . Granted, the obedience of Christ is an important element in Pauline theology. But there is not a shred of evidence anywhere else that he speaks of that obedience as Christ's pistis [i.e., 'faith']" (185).
Mark Seifrid also points out that "only five texts in the New Testament speak of the 'faithfulness of Christ' using the adjective pistos, a paucity which stands in stark contrast to the approximately 400 (both implicit and direct) references to faith in Christ in the New Testament" (Christ Our Righteousness, 140; see his extended discussion of this issue, 139-46).
Third, and on the other hand, "there is unambiguous evidence in the Pauline letters that Paul called for faith in Christ" (185).
Fourth, "the reading 'faith in Christ' also makes the best sense of the flow of thought in Rom. 3:21-4:12" (185; see his argument for this on pp. 185-86).
At this point, I find the arguments of Schreiner, Seifrid, and others who advocate the traditional view, convincing.