To understand the Reformed approach to this challenging question, we should begin with the concept of the "wills" of God. Reformed theologians typically refer to the relevant ones as the decretive (or "secret") and preceptive (or "revealed") wills of God, which R. C. Sproul defines as follows:
Decretive will: The sovereign, efficacious will of God
Preceptive will: The precepts, commands of God1
Reformed theologians point to a number of passages to establish this distinction. For the decretive will, here are a few examples:
Psalm 115:3: Our God is in the heavens; he does all that he pleases. [ESV]
Daniel 4:32: the Most High rules the kingdom of men and gives it to whom he will.
Romans 9:18: So then he has mercy on whomever he wills, and he hardens whomever he wills.
These passages describe a will of God that never fails and is independent of all other beings. But God's will is not always described in such terms:
Matthew 7:21: "Not everyone who says to me, ‘Lord, Lord,’ will enter the kingdom of heaven, but the one who does the will of my Father who is in heaven." [cf. Matthew 12:50]
Ephesians 5:17: Therefore do not be foolish, but understand what the will of the Lord is.
In these passages, it's clear that God's will refers to his commands and precepts, not his ordaining of events. The distinction is especially obvious when we consider biblical stories like that of Joseph being sold into slavery:
"As for you, you meant evil against me, but God meant it for good, to bring it about that many people should be kept alive, as they are today." [Genesis 50:20]
In this story, God's preceptive will is that Joseph's brothers love him and not sell him into slavery, as such an act is "evil." But God's decretive will was that Joseph be sold into slavery by his brothers so that many would survive the famine. Another example of this can be found in Acts 2:23, in which the "definite plan of God" (his decretive will) involved a clear violation of his preceptive will: his Son was killed by "lawless men."
Is the call of the Gospel part of God's preceptive will or his decretive will?
Turning now to God's will as it relates to the call of the Gospel, we must identify which "will" of God applies to passages like Matthew 11:28, in which Jesus commands people to come to him:
"Come to me, all who labor and are heavy laden, and I will give you rest."
Similarly, 1 Timothy 2:4 and 2 Peter 3:9 can be interpreted to refer to God's desire that all be saved.2
If this "desire" is a product of God's decretive will, then it would necessarily follow that all people will be saved. However, such an interpretation implies universalism, which seems to contradict other passages, like Romans 9:18 and Matthew 7:21 (quoted above), among many others. This desire that all be saved, therefore, cannot be God's decretive will, and so it must be his preceptive will. The commands to repent and believe are thus in the same category as the command to care for the poor: men can and do regularly disobey them.
How can a sovereign God allow his preceptive will to be violated?
Now we get to the heart of the issue, and hopefully it's now obvious that to the Reformed, this isn't merely a matter of explaining how man can reject the external call of the gospel—it's the broader issue of explaining the existence of evil. That is, we can reframe the titular question as, "How can [a good] God be sovereign if man can sin?"
This is, of course, a huge topic, which I've addressed more fully elsewhere. But ultimately Reformed theologians, while arguing that God is not the author of sin, and that man fell voluntarily, nonetheless hold that God ordained that sin would come into the world. That is, God's decretive will includes the sins of men, including their sins of unrepentance and unbelief.
Why would a good God do this? Charles Hodge suggests the following explanation, based on Romans 9:22–23:
Sin, therefore, according the Scriptures, is permitted, that the justice of God may be known in its punishment, and his grace in its forgiveness. And the universe, without the knowledge of these attributes, would be like the earth without the light of the sun.3
- Sproul, What is Reformed Theology?, p169
- Some Calvinists argue that the context in each of these verses does not require that "all" refer to every human being, but others consider that a possibility.
- Hodge, Systematic Theology, 1.5.13, page 435