Archibald Alexander on the atonement

"Here, then, we see what the nature of an atonement must be.  It must remove those obstacles which stood in the way of the sinner's salvation.  These arose from the law and justice of God, which demanded the life of the transgressor.  The Redeemer, therefore, must make full a satisfaction to law and justice, or the sinner cannot be saved.  He must render a meritorious obedience to the law which men had broken, and receive the punishment of their sins in his own person.  The sufferings of Christ were, therefore, of a strictly vicarious nature.  'He bare our sins in his own body, on the tree.'  'He died, the just for the unjust, to bring us to God.'  'He was wounded for our transgressions, he was bruised for our iniquities.'  'Our iniquities were laid upon him.' ... he died as an expiatory victim, a sacrifice to satisfy divine justice, as atonement for all the sins of his chosen, as a ransom to redeem them from their bondage;  yea, as a curse, to redeem them that were under the curse.  And this view of the atonement is vital to the Christian system.  It is plainly the doctrine of the Old as well as the New Testament;  and it ever has been the doctrine of every sound part of the Christian church;  and it would be easy to show, that the objections to it are either frivolous, or they are such as subvert the gospel of Christ, and bring in another gospel, which exposes the abettors of it to the anathema of Paul.  Gal. i. 8. 

All the sufferings of Christ should be considered as expiatory, and as constituting the atonement which he undertook to make for his people. ... And if it be asked for whom did the Redeemer bear all this, he has given the answer, 'I lay down my life for the sheep.'  He love his church and gave himself for it.  But his atonement, considered in its intrinsic value and suitableness, is infinite, and sufficient if applied, to save the whole world.

The sufferings of Christ, being those of a divine person, have an infinite value;  it follows, therefore, that although the punishment of the sinner was everlasting, yet Christ could exhaust the penalty of the law in a limited time." (Archibald Alexander,  A Brief Compendium of Bible Truth,  pp. 111-112, 113)

The vicarious sufferings of the God-Man Mediator are indeed of "infinite value."  And because they are vicarious and because they are of infinite value, they are NOT sufficient to save the non-sheep (e.g., non-elect, reprobate, goats, etc.).  I concur with the following statement about the type of hypothetical nonsense (e.g., "sufficient if applied") that Archibald Alexander speaks of:

"To say that Christ's death was 'sufficient' to save the reprobate is to put forth a hypothetical universalism. Jesus came to earth to save His people from their sins (Matthew 1:21), not make it possible for the reprobate to be saved in case they believed.

The atonement in no way, to no degree, enables God to show grace to the reprobate. The atonement is just that -- the atonement. Atonement means reconciliation. Christ's blood atoned -- it achieved reconciliation between God and the people for whom Christ died (2 Corinthians 5:19). It did absolutely nothing for the reprobate.

God's grace is His unmerited favor. Where there is no imputed righteousness, there is no favor. God is holy; he cannot show favor toward anyone who is not as holy as He is. The only ones to whom He shows favor are those who have been covered with the imputed righteousness of Jesus Christ." SOURCE