Biblically, the answer is yes. Christ died for everyone. You, me, everyone; your sins, my sins, everyone's sins.
That doesn't mean everyone will be saved. But Christ didn't die only for the elect, Christ died for everyone.
Both the Calvinist doctrine of Limited Atonement and the Arminian doctrine of Unlimited Atonement, effectively, argue that Christ only dies for some. The difference is that the Calvinist says that on account of man's total inability, God's unconditional election, and God's irresistable grace the elect will be saved, and those whom God predestined to salvation are those for whom Christ died; while the Arminian says that we aren't totally unable, God's election isn't unconditional, and grace is resistible, and so Christ died for all who would believe in Him by their own decision and choice.
Approaching the topic from entirely outside the Reformed theological paradigm, as a Lutheran, it is neither Limited nor Unlimited Atonement, but Universal Atonement. Christ died for all. Full stop. Everyone. That's why St. Paul can say in Romans 5:18 that all are justified. This is Objective Justification, what happened objectively once and for all, for everyone, by Christ's death and resurrection. Subjective Justification is what happens when, by the grace of God, through the means of His grace, He gives us faith and appropriates to us all which Christ accomplished. This is is a big part of what St. Paul says in Romans ch. 10, asking how can those who never heard of Him call upon Him, and how can they hear unless one is sent to preach. Thus, the Apostle says, faith comes by hearing and hearing by the word of Christ (Romans 10:17). It is therefore the preaching of the Gospel which God has chosen to be the means by which what Christ has done comes to you and to me, it is for this reason that Christ called His apostles to preach the forgiveness of sins in His name beginning in Jerusalem, and commissioned His Church to preach the word, and to baptize.
As Martin Luther poignantly states in the Large Catechism,
"For neither you nor I could ever know anything of Christ, or believe on Him, and obtain Him for our Lord, unless it were offered to us and granted to our hearts by the Holy Ghost through the preaching of the Gospel. The work is done and accomplished; for Christ has acquired and gained the treasure for us by His suffering, death, resurrection, etc. But if the work remained concealed so that no one knew of it, then it would be in vain and lost. That this treasure, therefore, might not lie buried, but be appropriated and enjoyed, God has caused the Word to go forth and be proclaimed, in which He gives the Holy Ghost to bring this treasure home and appropriate it to us." (Large Catechism, Section II, Article III, 38)
The work is done and accomplished. Christ's work is finished, it is perfect, complete, and it is for every man, woman, and child. Not merely as a potential, but objectively so. But for us to benefit from this work it must come to us as individuals, that is why Christ institutes His Church and calls her to the ministry of Word and Sacrament. That God, through His Gospel, brings the all-sufficient work of Christ to you and to me. The Gospel is "Christ died for you" not "God did His part, now you have to do yours."
And thus, yes, Christ died for those who reject him. Because, frankly, that describes everyone. Even those of us who call ourselves Christians reject Him, we reject Him every time we sin. How often in our lives, in thought, word, or deed we--like Peter--deny the Son of God? Yet, St. John reminds us, "If we confess our sins, He is faithful and just to forgive us our sins and cleanse us from all unrighteousness."
Christ died for all. Those whom God predestined from before the foundation of the world, and those who, even on the Last Day, would deny and curse Him.
Which is why damnation is not God's work against man, but man's work against himself. It is only by the will of man that he is damned, for he chooses himself even to his own destruction. To borrow language from C.S. Lewis, what may have begun as merely a grumble inside a person ultimately makes them the grumble. A shrinking away from God, and thus away from all that makes us human, to become nothing more than the grumble. So horrid is this that St. John of Patmos can only describe it as "the second death", using the imagery of a burning lake of sulfur and fire into which even death and Hades themselves are cast into. A death that is more than death.
-CryptoLutheran
