John Piper describes one element of saving faith, and laments the spurious faith held by some:
What does faith receive in order to be justifying faith? The answer, of course, is that faith receives Jesus. … But we must make clear what this actually means, because there are so many people who say they have received Christ and believed on Christ but give little or no evidence that they are spiritually alive.
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One way to describe this problem is to say that when these people “receive Christ,” they do not receive him as supremely valuable. They receive him simply as sin-forgiver (because they love being guilt-free), and as rescuer-from-hell (because they love being pain-free), and as healer (because they love being disease-free), and as protector (because they love being safe), and as prosperity-giver (because they love being wealthy), and as creator (because they want a personal universe, and as Lord of history (because they want order and purpose).
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Such a “receiving of Christ is the kind of receiving an unregenerate, “natural” person can do. This is a “receiving” of Christ that requires no change in human nature.
John Piper, in Think: The Life of the Mind and the Love of God.