I've been reading E.P. Sanders book, Paul and Palestinian Judaism, which I heartily recommend to any Christian.
At the beginning of the book, Sanders lays out the history of Christian explanations of Judaism in the time of Christ. It is a quite harsh critique, which I am not in any position to judge, describing how Weber (late 19th century) wrote about Judaism in Jesus day based mostly on books that Judaism never considered authoritative and ignored completely the writings of early Rabbinical Judaism.
Then, later writers simply built on Weber's work, ignoring Jewish scholars (who had far better understanding of the relevant material) who challenged their views. Sander's view is that Christian Writers engaged in virtually felonious acts of ignoring primary source texts and the work of dissenting academics. As I mentioned, I'm not really in a position to judge the specifics, but it is a fascinating critique.
The basic point Sanders makes it that, contrary to what Christians regularly claim, writing during the early Rabbinic period does not indicate a legalistic religion where Jews try to "earn" their salvation through good works, nor does it point to a religion where the highly codified law led to only external, surface fealty rather than an internal desire to please God.
One point in which Sander's views match my own is the idea that Christians have so misconstrued questions regarding salvation that they simply cannot understand Judaism on its own terms. For example, Christians assume that "The Law" describes what one has to do perfectly to find favor with God. Thus, since no one can keep the Law perfectly, no one can find favor with God (on his own).
But for the Jews the Law does not answer the question "what must one do to find favor with God?" Thus, the whole line of reasoning is wrong-headed on its face, and the question "do you think you can earn your salvation on your own?" is ill-posed.
Sanders claims that the Law was simply understood as what God, as King, ordered, and the keeping of the law was done for two reasons:
1. Confirming the Law is tantamount to affirming God as King (i.e., the one whose right it is to give the Law).
2. The doing of the Law is the natural response of Israel given that the Spirit of God resides in their midst.
The first point is strikingly close to Christ's question "Why do you
call me Lord and not do as I say?" or "I tell you the truth, not
everyone who says 'Lord, Lord' shall be saved."
To modern, "what's-in-it-for-me" humans, the second point is easy to misconstrue. I'm not even referring to gratitude here but rather the notion that God is holy, and so it is only natural to desire that the land where God's Spirit resides be clean, and the Law explains how to bring that about. Think of it as an appeal to one's cosmic sense of appropriateness.
It is unsurprising that Christians in general have a hard time understanding this because of our fixation on "how do I get to heaven?" But Judaism's roots came before there was any belief in an afterlife, and the Jews, in any event, didn't have Augustine (or Martin Luther) to try to tell them that they start out life deserving only everlasting torment.