After some discussion, I’m finding that I have to explain what I mean when I say that the rarer form of unprepared heart for the Gospel is despairing sin.
Recall that my central understanding of the Gospel is that is at heart about the glory of Jesus Christ and the reign of His kingdom (Matt. 4:23). Jesus Christ rules over all things (Rev. 11:15), and that rule is evidenced both in wrath for sinners, and just mercy on some that was purchased on the cros (Rom. 9:22-23).
The problem for the exceedingly rare despairing sinner is not the conviction that they are sinners. They already have that. The problem for the despairing sinner is that the rule of a just omniscient God comes as bad news to this person. They are in rebellion to such a God, and know that they are, and so upon learning that there is such a God, despair because they cannot hope to measure up.
Unless their hearts are prepared, the death and resurrection of Jesus Christ for their sins is going to simply be too good to be true. They will prefer to have some mediating priesthood or action, or something, so that they can be sure that God is actually for them and not against them.
Biblically, this is the group Jesus and the apostles had the most success with at the get go. The only thing that the Spirit needs to convince such people is the love of God and the objective truth of Christ’s death and resurrection for their sins. In societies with a strong basis in an objective morality, the preaching of God’s love through the cross will be effective.
However, this group is very rare in modern culture. In fact, I’ve only ever met a handful of this group. In order to be in this group you have to have enough of a background that would convince you both of the reality of objective morality and that you are in transgression of that. Since the first step is openly denied in modern western culture, it is going to be rare to find people who are convinced that they are in transgression of it. What few that do get past that step, run up against the modern imperial I, and the belief that the objective morality is personally defined (thus everyone is always completely moral, since they define morality).
That is why I believe that Phariseeism is the far more common opposition to the Gospel in modern hearts, and why I believe that the current focus on the truth of God’s love to the exclusion of God’s wrath is probably doomed in modern society.