The first thing that must be pointed out is that confessional Protestants actually agree with this statement (remember: we're all about the Bible). The real question is not whether the principle of justification by works is true, but for whom it is applicable.
Reformed theology teaches that:
The first covenant made with man was a covenant of works, wherein life was promised to Adam, and in him to his posterity, upon condition of perfect and personal obedience (Westminster Confession of Faith VII.2).
In the garden, Adam was both able and expected to obey his Creator which, if he had succeeded in doing so, would have brought about his glorification and entrance into eternal Sabbath rest based on that obedience. Now we all know the story, how that he failed and fell, plunging us all into sin and misery. This is why the Confession goes on from the covenant of works and expounds the covenant of grace, according to which sinners receive the life that Adam forfeited, only now through the work of a second Adam, Jesus Christ.
Now if you're wondering where this structure and movement from works to grace comes from, look no further than the book of Romans. The obedience according to which man will be justified in 2:13 is speaking of the just demands of God upon all people by virtue of the original creation covenant which are still incumbent upon the sons and daughters of Adam.
Now if we keep reading in Romans we see, of course, that no man can perform the "works" that we need to be justified: "For we charge that all, both Jews and Greeks, are under sin, as it is written, 'There is none righteous, no, not one'" (3:9-10).
The good news, therefore, is not that God will recognize our works and justify us, but that he will reckon the work of Christ as our own and save us based upon the labor of Another: "But now... the righteousness of God through faith in Jesus Christ [is revealed] for all who believe."
Again it appears that the attempt to couple faith and works for justification fails the exegetical test (especially since Paul will go on to say that justification comes "to him who does not work, but believes").
And yes, we will get to James 2 eventually, so hang in there....