Redemption available and redemption applied are two different things. God provided the Passover lamb, but each Jewish family needed to pain their doorposts with the blood for themselves. The lamb's blood didn't save them by just sitting there in the bucket. If Christ didn't provide redemption for everyone, than God could not offer salvation to everyone (which He does) and not be a liar in so doing. As isaiah said, all we like sheep have gone astray; each one of us has gone to his own way, but the Lord has laid on Christ the iniquity of us all. The "all-we" who went astray = the "us" whose iniquities were laid on Christ. You aren't lying when you say to an unbeliever, "Christ died for your sins." In fact, you sound just like Paul, who taught that very thing to the unbelieving Greeks (1st Cor. 15:3).
Jack is the teaching elder of Ironworks Pike Community Church. He is a graduate of Columbia Biblical Seminary http://www.ciu.edu.