Many think that to share the gospel with non-Christians requires that we tell them, with confidence, that Jesus died for them. John Piper posts a great little conversation showing how a Christian who embraces definite atonement (the view that Jesus Christ died specifically for all those who would ever trust in him, love him, and obey him) might go about sharing his faith with a non-Christian – and why (in my opinion) it is actually more understandable and more compelling.
An excerpt (U is an unbeliever, and E is an evangelist):
U: Did he do that for me?
E: If you will have him—receive him—you will have all that he is for you and all that he did for you. If you will trust him, yes, he did it for you.
U: So you don’t know if he did it for me?
E: He is offering himself to you right now freely. He is offering you a wonderful, finished work of redemption—all that he accomplished in absorbing God’s wrath and cancelling sins. All of that is yours for the having, right now. If you won’t have it, it’s not yours. If you will, it is. There’s only one way to know if your sins were cancelled and your death sentence was commuted in the death of Jesus. Believe on him. His promise is absolute: If you believe, you will be saved. If you won’t believe, you remain in your sin, and under God’s wrath.
Read the whole thing – keep in mind that the dialogue is meant to draw out a theological point (admittedly, many if not most non-Christians would not think to ask such precise questions). If this topic intrigues you, I highly recommend a detailed look at the language in John’s gospel (the most evangelistic gospel, and also the one that, in my view, most emphasizes God’s decisive role in our salvation). The phrase often used in John is “those given to me (Jesus) by the Father” — e.g., John 6:37, 6:39, 10:29, 17:24-26, etc.
My understanding is that Piper just completed a chapter on definite atonement for a forthcoming publication.