1) God doesn't force the man to drown ( sin ).
2) Man loves the water ( sin and sinning ) ( Romans 1:18-32, John 3:19-20 )
3) Man hates the rescuer and will not accept the life ring, because that would mean leaving the comfort and love of the water.
4) Man reaching out to take the life ring, is not only impossible from the man's standpoint, it's the last thing he wants to do.
5) So, God has to jump in, swim over, knock him unconscious to keep him from struggling and place the life ring around him and then haul him back to shore.
Then he takes the man He just rescued, dries him off, takes him home and gives him new clothes and sits him down to dinner in a dining hall fit for a king.
That's about as close an analogy as I can come up with.
Dave, I can appreciate your analogy but perhaps there is another way to look at it. God changes the sinner and makes him into a new creature (2 Corinthians 5:17). This unilateral work of God is regeneration, in which the sinner is passive (Ephesians 2:4-5). Once regenerated (and now spiritually able), the now-former-sinner wants nothing more than to come to God. This is the biblical way of viewing it because the Elect are justified by faith.