Following are some quotes from Dr. Daniel's September 2010 sermon on Limited Atonement.
"There is a general aspect of the atonement of Christ for all. Now, even the best Calvinist theologians will admit, yes, there is a general aspect to the atonement before we look at the particular aspect. For example, because of Christ's work on the cross there is a delay of judgment for sinners. Think about that. We deserve to be punished, we deserve to be hauled in before God's bar of judgment long ago. The fact that we are still alive here on earth is due to the work of Christ on the cross. In the same way, the fact that we are not in hell right now. There has been a stay of execution - not a pardon - but a stay of execution because of Christ's work that has delayed judgment and hell for people now. Even for those that will end up in hell, the delay right now whereby God is pleading with them is due to the work of Christ. It's a temporary reprieve."
"... there is common grace. There is a general love of God. Jesus talked about the bounties of health, family, friends, happiness. Rain falling on the just and on the unjust, common grace, the bounties and beauties of creation - all flow to us through the cross. And Christ has purchased those for everybody, elect and non-elect, sinners and saints, and for everybody."
"... there is a free offer of the Gospel that can go out to all . . . the atonement of Christ has provided more than enough for everybody, and He sends Christians out with the free offer: 'Come, for all things are now ready.'"
"Now some scholars will say that this universal aspect of the atonement can be seen in verses such as John 3:16, 'the world,' I John 2:2, 'the whole world,' II Cor. 5:14, 'all,' and other ones, and I see that there is some truth in what they are saying."
"Because Jesus Christ is God and not simply man, what He did on the cross has infinite value and universal sufficiency. Now, the theologians have come up with a formula for this. Now I want to say it and then repeat it, because you might miss it, but it's very important. All that Jesus did on the cross would have been necessary for the salvation of only one person. One person committing only one sin would still require an infinite payment to the Father. However, Jesus would not have had to suffer more even if there had been a million times as many human beings to be saved, because Jesus made an infinite satisfaction to the Father. And that would have been required if there had been only one person or if there had been ten million times as many people as there have been in human history. So however many there are to be saved, Christ paid a sufficient amount for everybody because His atonement had infinite value. It's not that if one more person had to be saved Christ would have had to suffer more or die a second time. It's finished. He paid an infinite price, and in that sense you can say it has general implications for everybody."
"Jesus Christ died in a special way only for those that God had elected to salvation. This does not deny the general aspect . . . some have put it like this: in the general aspect Christ did some things for everybody, but in this aspect He did everything for some people - those that He had chosen."
"... human beings are unable to save themselves, but God has chosen some people to be saved, and because they have been chosen Christ did something especially for them. Now, this does not deny a general aspect of the atonement. It's concentrating on a special aspect that guarantees their salvation. That's why it's sometimes called particular redemption, for the elect in particular. It's limited in scope, not in value. It has a specific purpose for them. There is a general purpose, but there is a specific purpose."
"... although it's provided for all in one general sense, it's guaranteed for the elect in a special way. Now, as I said before, the special aspect or intent of the atonement is sometimes misunderstood. And so the theologians will compare Scripture and Scripture, and the formula that has generally emerged is something like this: Christ's death is sufficient for all, but it is efficient only for those that have been chosen, and those are the two aspects . . . By the way, you can see that 'for all, but especially for some' even in Scripture. I Timothy 4:10 says that Jesus is, quote, the Savior of all mankind, especially of those that believe."