Sometimes I will hear a Calvinist, in response to the question whether or not God loves all men without exception, distinguish between types of God's love. For instance: God has a love for those He has destined to constitute the church, His bride, that He does not have for reprobates.
However, this doesn't answer whether or not God loves reprobates. Indeed, emotional considerations aside (not many people like to talk about God's hatred of sinners &c., I get it), it is not clear as to how one could argue God loves reprobates. We know that God loves some who are as yet unbelievers, but there is a reason God loves them which cannot be ascribed to the reprobate: God sent Christ to die for them. Remember how God's love is demonstrated towards the elect:
Romans 5:8 God demonstrates his own love for us in this: While we were still sinners, Christ died for us.
1 John 4:10 In this is love, not that we loved God, but that He loved us and sent His Son to be the propitiation for our sins
God didn't send His Son to be a propitiation for all wicked men. He sent Christ to be a propitiation for the wicked elect. In what way, given the limited scope of intention for the atonement, could it be argued that God loves reprobates? Common grace is what one would suspect the answer to be. The idea of common grace is pretty common in Christendom, I think; the idea is that by simply letting one who is guilty of sin live (and not only live, but reap many so-called benefits like health, perceived happiness, etc.) when he deserves to die, God must be being gracious to them.
But what is grace? Unmerited favor. The "common grace advocate," then, is suggesting that God is displaying favor to or gracing the reprobate by allowing him to live &c. But I fail to see how this is favor. In fact, the fact that such alleged benefits will actually bring greater condemnation on the heads of the reprobates indicates precisely the opposite, for to speak of God "favoring" someone who not only will be condemned for the failure to make proper use and give proper thanks for that benefit which is said to evince God's favor but also has been unconditionally predestined by God unto such greater condemnation for having experienced that alleged benefit (also predestined) proves that it is not favor at all; thus, it's not grace at all. It makes no sense to view a temporal [perceived] benefit as an evidence of God's favor, given that such will actually and was predestined to necessarily yield greater condemnation for having experienced and rejected proper use of that benefit.
I could end the post at this point, but it is both instructive and uplifting, I think, to consider the parallel; if God's disposition to the reprobate is conditioned on who He has purposed them to be (condemned by sin), it makes sense that God's disposition to the elect is conditioned on who He has purposed them to be (justified and glorified in Christ).
Why is this important? Consider a generic unbeliever. Does God love him? How would you know? What would it mean for God to love an unbeliever?
I believe the idea that "God works together all things for one's good" (cf. Romans 8:28) is as good a definition as any to describe what is meant by the statement God loves an individual. Now, does God work things together for God for all men without exception? No - the elect alone. Did the demonstration of God's love - Christ's sacrifice - apply to all men without exception? No - the elect alone.
There is a correlation, then, between God's love and God's election or (equivalently) between God's love and who God has purposed the elect to be: justified and glorified in Him. For that reason, the above question - does God love the generic unbeliever? - is too vague. It is wrong to abstract God's love (or lack thereof) for an individual from God's purpose for him. To do so not only makes it impossible to give a coherent answer as to whether or not God loves all unbelievers, but it would be furthermore impossible to give a coherent answer why or how God can even love the elect unbelievers. As I've written elsewhere:
//Only if one accepts that God chose to elect men in Christ before He decreed the Fall does it make sense that a holy God can choose to save a people deserving of wrath: because they, the elect, had already been chosen to be vessels of mercy.//