Having truly and plainly showed our sinfulness, wretchedness, and cursedness by nature, I come unto the remedy, our redemption by Christ. And God forbid that He should create man, the best of His creatures, for destruction! "What gain and profit is there in our blood?" (Psalm 30:9). God is full of grace and compassion, and He considers that we are but dust. And happy are we that we are but dust. Had we been more glorious creatures, like angels, we would not have had the benefit of a Savior. When they rebelled, God considered their makeup; and as with a high hand they rebelled, "so the Lord reserved them in everlasting chains under darkness unto the judgment of the great day" (Jude 6; 2 Thessalonians 1:9). They fell without a Redeemer. It is well for us that God considers that we are but dust. By Jesus Christ He saves us from the wrath to come. It would have been better for us never to have been born than to be born firebrands of hell.James Ussher, "The Satisfaction of Christ," in The Puritan Pulpit: The Irish Puritans, ed., Don Kistler (Orlando, Florida: Soli Deo Gloria, 2006), 116–118.
But the point is that we are "brands plucked out of the fire" (Zechariah 3:2). It is fitting, therefore, that we should know who our Redeemer is. It is Jesus Christ, and here consider that Christ Jesus offered for us for the satisfaction of God's justice, and this is His priestly office.
Also, as there was no remission without shedding of blood, therefore after the blood is shed and the priest offered Himself, there comes a second thing, or else we would never be the better. Christ offered Himself to us, and this makes up our comfort. Many talk of the extent of Christ's death and passion, saying that He died sufficiently for us, which is improper. For what comfort would it be that Christ was offered for us if there were no more? A bare sufficiency in Christ does not serve the turn; this would be a cold comfort. Suppose a man who was in debt, afraid of every sergeant and every sheriff, should be told, "Sir, there is money enough in the king's account to discharge all your debts." This may be very true, but what good is that to him? What comfort does he have by it unless the king offers to come and freely assume his debt? And it would be a cold comfort to us to know that Christ is sufficient for us unless He invites us to take freely of the waters of life. But "Ho, every one that thirsteth, come ye to the waters" (Isaiah 55:1). Thus, unless Christ is offered to us as well as for us, we are never the better.
Now to make this more clear, observe that in every sacrament there are two acts of the minister. The first one has relation to God; it is a commemoration of the sacrifice, in which respects the ancient fathers called it a sacrifice. The other is the breaking of bread and pouring out of wine, wherein there is a commemoration of the broken body and the shed blood - not as they are concomitants, the wine in the bread, as the foolish papists dream, for that would rather be a commemoration of His life, when the blood runs in the veins, than of His death. The commemoration of Christ's death is made by separation of the blood from the body, and as there is one act of the minister in consecrating by breaking the body and pouring out the blood, so there is a second act that is ministerial. When the minister says, "Take, eat; this is My body," it is as if Christ were present, saying, "Come, take My body." You have as free an interest to it as when you are invited to your friend's table you have a right to the meat before you. So that as Christ is offered for you, so He is offered to you. And what now should hinder you, unless you are one who will obstinately oppose your own salvation, and say, "I will not have this Man to rule over me." You cannot miscarry. But if you will be your own lord, then you must perish in your infidelity. Here are the keys of the kingdom of heaven given unto God's ministers, unless you willfully oppose your own salvation and shut the door of salvation which Christ has opened so wide for you. The ways of God are plain. Christ has paid a great price for you, and then, as great as it is, He offers it to you.
When Ussher says that some say "that He died sufficiently for us, which is improper," he's talking about those who merely teach an internal or bare sufficiency. He's not saying that the formula "sufficient for all, efficient for the elect" is improper. He's just saying that some conceptions of that formula are improper, and that it offers no real comfort for the despairing sinner. What good is it for sinners to know that Christ, the great King, has infinite worth (enough money in his account, so to speak)? They must know, as Ussher says, that the bible teaches that he suffered sufficiently for them (the money has been put down for them that they might be released from their debt, but in a conditional way). Thus, Christ is offered for them and to them in particular, but it will do them no good if they do not believe.
For more on Ussher's classical conception of Christ's sufficiency (i.e. an ordained sufficiency as opposed to a bare sufficiency), see John Davenant's Sufficiency Distinctions.