The Satisfied Lamb
Matthew 1:21 - you shall call his name Jesus, for he will save his people from their sins.
Isaiah 53:8 - By oppression and judgment he was taken away; and as for his generation, who considered that he was cut off out of the land of the living, stricken for the transgression of my people? 9 And they made his grave with the wicked and with a rich man in his death, although he had done no violence, and there was no deceit in his mouth. 10 Yet it was the will of the Lord to crush him; he has put him to grief; when his soul makes an offering for guilt, he shall see his offspring; he shall prolong his days; the will of the Lord shall prosper in his hand. 11 Out of the anguish of his soul he shall see and be satisfied; by his knowledge shall the righteous one, my servant, make many to be accounted righteous, and he shall bear their iniquities.
Ephesians 5:25 - Husbands, love your wives, as Christ loved the church and gave himself up for her...
Rev. 5:9 - for you were slain, and by your blood you ransomed people for God from every tribe and language and people and nation
Christ's work on the cross achieved all of the Divine purposes for it. The intent of the design was not merely to try to save all, but when all was said and done, the plan could fail for many because of that stubborn thing called "free will," with the Savior sad for all eternity because many He died for received no benefit for all His labor. No, He died a satisfied Savior, giving Himself for His friends, for His sheep, for His people, for His Church, and fully accomplished the work of redemption for all in this number.
All who are particularists (who believe that not everyone will be saved - that some people will in fact spend eternity in hell) believe in some type of limitation to the atonement of Christ. The Arminian limits its power, for it only becomes effectual through man's cooperation; the Reformed person limits its extent. As C. H. Spurgeon said, "The doctrine of Holy Scripture is this, that inasmuch as man could not keep God's law, having fallen in Adam, Christ came and fulfilled the law on the behalf of his people; and that inasmuch as man had already broken the divine law and incurred the penalty of the wrath of God, Christ came and suffered in the room, place, and stead of his elect ones, that so by his enduring the full vials of wrath, they might be emptied out and not a drop might ever fall upon the heads of his blood-bought people." (Sermon 310 - "Christ our Substitute - New Park Street, Southwark)
Elsewhere he preached, "I had rather believe a limited atonement that is efficacious for all men for whom it was intended, than an universal atonement that is not efficacious for anybody, except the will of man be joined with it." (Sermon number 173 - Metropolitan Pulpit 4:121)
In another sermon, Spurgeon said, "Once again, if it were Christ's intention to save all men, how deplorably has He been disappointed, for we have His own evidence that there is a lake that burneth with fire and brimstone, and into that pit must be cast some of the very persons, who according to that theory, were bought with His blood. That seems to me a thousand times more frightful than any of those horrors, which are said to be associated with the Calvinistic and Christian doctrine of particular redemption." (C. H. Spurgeon - Sermon 204 - New Park Street Pulpit 4:553)