I have to write a final paper on any topic on apology, forgiveness or reconciliation. I have chosen to focus on some of Jesus' last words which were "Father forgive them, for they know not what they do." I interpret the last preposition phrase to mean that if the persons who crucified Jesus knew what they were doing was wrong, they should not be forgiven. In other words, I believe Jesus would NOT forgive an unrepentant sinner.
First, a minor logic problem. That he asked the Father to forgive them because they didn't know what they were doing doesn't necessarily mean he wouldn't if they did. There might be some other valid reason to forgive them if they do. The blasphemy against the Holy Spirit is the only thing that Jesus put beyond forgiveness. Even high-handed sin, while it may guarantee you a good beating, is not unforgivable.
Leading up to this question is the point that it's prudent to find excuses to forgive people, and to avoid reasons not to if we are justly able to - as the proverb says, "A prudent man ignores an insult." Thus Moses writes in Leviticus 19:18, "You shall not take vengeance, nor bear any grudge against the sons of your people, but you shall love your neighbor as yourself; I am the LORD." So as far as forgiveness means dropping grudges, it extends to pretty near everybody. I know we can follow the example of the scribe in Luke 10:29, who wishing to justify himself, said to Jesus, "And who is my neighbor?" and ask, "Who are the sons of my people?" But the context doesn't seem to recommend it.
Leviticus 19:18 concludes with "I am the LORD," not an afterthought, but a statement of how this happens. Dropping grudges is one of those good and perfect things that comes down from above; we don't get to generate it in our wonderful selves. This looks like a command, but it's really a promise. Loving my neighbor as myself in this case means that since I don't want people, and God, to hold grudges against me, it would be prudent to quit doing that myself. The sanity to see and act on that is a real gift from God.
This sort of forgiveness extends to everyone, and it has a sharp end. When Romans 12:19 says, "Never take your own revenge, beloved," it goes on to say "but leave room for the wrath of God." What's wrong in this verse with executing our own wrath is that this denies room to God's wrath against the perp. This leads us into the call in the next chapter to submit to authorities. When the authorities are unjust, it takes God-sized wrath to handle it, and you don't want to get in the way by trying to settle up with them yourself.
In short, this dimension of forgiveness is not to acquit anybody, or necessarily to expect a relationship. Even if he hurt you, you don't have jurisdiction, so you're turning him over to God's court, and pouring him out of yours. As David said to God, having degraded Bathsheba through the implied threat to murder her husband and then murdering him anyway, "Against you only I have sinned, and done evil in your sight." In God's court, he may find mercy, or he may encounter judgment, and we can live with it either way, because God does no injustice in the end, even if he puts up with it for a while.
On the cross, Jesus spoke of a different level of forgiveness, which leads to a positive relationship. The example he was following was Job, whose captivity was turned when he prayed for his three friends, who went to Job when God told them to if they knew what was good for them (Job 42). Jesus addressed the same question in his parable of the king and the unmerciful servant (Matthew 18:21-35). Here, when someone actually comes to you for forgiveness, then you forgive him because you'd like God to forgive you when you need it.
All of this gets badly tangled up when we mix it up with trust. Forgiveness is free, but trust is earned. Doesn't matter what, if anything, I forgive the two-year-old for, or even if there's anything to forgive. I don't trust Twosie to carry the glass of wine over the white carpet, or to parallel park the car.
Lots of times, I've seen people feel that they can't forgive because they then feel obliged to trust. And people will manipulate forgiveness to get trust. "If you forgive me, why don't you trust me?" Well, player, because you're demanding to be trusted, and people don't do that when it's safe to trust them. If I forgive you, I'll let you earn my trust, but if you want me to actually trust you, you still have to earn it.