Being omniscient, God not only has the past, present, and future in His mind, but also all possible realities. God not only knows what has happened, but also what could have happened under different circumstances. And, while hypothetical, God does occasionally give us insight into those alternatives.
For example, in the current reality, Tyre, Sidon, and Sodom have all received their final judgement. The cities were destroyed, and the sinners within them were long dead by Jesus' time. However, in Matthew 11:21-24, Jesus tells us that had He performed His miracles there, those cities would have repented, and the disasters God brought upon them would never have happened.
This alternative scenario poses several problems for Calvinism, particularly for Total Depravity and Limited Atonement. Note, first of all, that the sovereignty of God remains fully intact. Though it was entirely possible for God to save these cities, He opted not to do so. Nevertheless, the fact is He could have saved them purely by revelation and demonstration. The very same revelation and demonstration resisted by the people of Chorazin, Bethsaida, and Capernaum.
This is troublesome for the doctrine of Total Depravity, which states that the human condition is so depraved that man is incapable of coming to God of his own free will. Of course, God must always make the first move. We can know nothing of Him but for revelation, and so without those revelations, we obviously cannot come to faith (Romans 10:14-17), regardless of our own free will. Nevertheless, once that revelation has been received, we are free to choose (and of course, are responsible for) how we will respond. You can reject the will of God (Luke 7:30), but Jesus tells us the three cities would have repented.
Further problems for Calvinism are caused by the fact their repentance would have apparently been effective. This is problematic for Limited Atonement, for even the most penitent of sinners can make no atonement for himself. Only one sacrifice is effective for all: The cross. Thus, if God would have forgiven these three cities, the cross must have covered them. Yet, though all evidence suggests it did, it did not become effective for them, as they never repented nor came to faith, and were destroyed.
From the cities of Tyre, Sidon, and Sodom, we see that neither Total Depravity, nor Limited Atonement, are solid doctrines. Questions are raised that Calvinism simply cannot adequately account for. In the end, salvation seems to be a genuine gift that can be accepted or rejected by all to whom it is offered, yet Scripture clearly tells us it is offered to the whole world, not just to the elect, and that even those who are not elect have the ability to accept it. They merely reject it, which is why they are held accountable. Total Depravity and Limited Atonement simply cannot account for these three cities.