It takes two to reconcile

Reconciliation is by definition a two person event.
It's hard to understate the force of this statement, or the consequences that must have on our understanding of theology.  Moderate Calvinism, which asserts that God has procured salvation for all men upon condition of belief, is the only workable idea given the nature of reconciliation, a process whereby both God and man come together.

Before our relationship can be restored, God, as the injured party, must first be willing (or in this case, able) to forgive. Because He is a just God Ps 111:7, and His justice demands punishment upon sinful men, Is 13:11, His wrath must first be appeased.
The word ἱλασμός rendered propitiation most nearly speaks to this, that the only way God could be finally appeased was by the perfect sacrifice of Christ.  It's the word in 1 John 2:2- Jesus has made a propitiation not only for our sins, but for the sins of the whole world. 
The hyper-calvinist take this verse to speak exclusively of the elect, that is, Jesus atones for the sins of the elect, and not only the elect, but the elect as well, but it's not conceivable that this sin offering to God would be good for only the elect, because it satisfies the justice of God, and in a sense moves God from unwilling to forgive, to willing. It is not to man, but to God that propitiation speaks.  God's wrath is satisfied, not mans sinfulness, for if that were the case we would be saved apart from faith.
That the Bible speaks about the forgiving disposition of God indicates this principle as well, Eze 18:23, Eze 33:11, Jer 27:17, Luke 13:34 speak of God as pleading for men to come back, which indicate that His fierce wrath has been in some way appeased. Therefore God can earnestly desire the salvation of all men, 1 Tim 2:4 not merely the elect, because He invites all, having removed the debt against them as long as they draw breath. The offering Jesus makes on the cross being toward God, as a man, is therefore to the benefit of all men.

For their part men must want to come back before they can be reconciled, which is why God urges men to take freely of the water of life, to come and experience the free gift, Rev 3:20, to turn and be saved.  Men demonstrate their return to God by possessing faith, by putting their trust in Christ, by doing what He has demanded of them John 6:29, and since all men have the natural ability to do this, all men may be benefited and saved by the death of Christ. In other words, God invites all to return because all men can return, and when they do both they, and God, have come together for reconciliation.

Once both sides have been brought together, they have between themselves reconciliation, the word in Romans 5:11, or 2 Cor 5:18 καταλλαγή, which speaks to a final, ultimate, peace between God and the saved.
It is here only that we may make the distinction between elect and non-elect, and we can say whether or not Christ's blood is of ultimate benefit or not. The elect are the ones who by God's secret council and power come back because they desire God, the reprobate are the ones who don't. 
Which leads me to the bottom line of the post: although there is reconciliation only between the elect and God, we must be careful that we don't assert the atonement, which is part of the equation, is only for the elect.