We emphasize works often enough in the church, it is easy to see how anyone can come to that conclusion. Our 3rd Article of Faith says, "We believe that through the Atonement of Christ, all mankind may be saved, by obedience to the laws and ordinances of the Gospel." Nephi in The Book of Mormon says, "we know that it is by grace that we are saved, after all we can do." And we will also cite James 2 supporting the need for both, for "faith without works is dead."
What doesn't get emphasized in the church often enough is Ephesians 2: "for by grace are ye saved through faith; and that not of yourselves: it is the gift of God: Not of works, lest any man should boast." We do believe in the Bible, don't we? So what about this verse? Clearly James and Paul had two different audiences; I don't think Paul is saying that "by grace are ye saved through dead faith."
But the message is clear: It's what Christ did that saves us, not us. Nephi's message would be entirely different if he said, "we know that it is by all that we can do that we are saved, after receiving grace." But if works don't save us, what are they good for? We are saved by the grace of Christ, but we are judged and rewarded by our works.
This concept is described wonderfully in a BYU devotional I was recently shown given last year by Brad Wilcox: His Grace is Sufficient
My favorite line has got to be:
“Jesus doesn’t make up the difference. Jesus makes all the difference. Grace is not about filling gaps. It is about filling us.”He says a lot about works, and basically says that there's still plenty for us to do, but it is for a totally different reason than salvation. It is to show our gratitude for Christ, to change ourselves and to prepare for life in heaven.