It depends on the purpose of Christ’s death. Jesus died so that all might be saved (through His death the salvation of man is made possible, He is the propitiation for our sins – not only ours but for the sins of the world; He is the savior of all men, especially those who believe). Jesus died in obedience to the Father so that man might be saved. All the Father gives will come. Jesus died for His sheep (given by the Father), He lay down His life for the Church. While Jesus’ death made possible the salvation of man, He did not die so that all men would be saved. To the unbeliever, the Cross is a provision of salvation. To the saved, the Cross effects salvation.
Here's an illustration (‘cause we love illustrations):
God sent venomous serpents among the Israelites, and when they were bit they died. He commanded Moses to make a bronze serpent and set it on a pole. When a man was bitten, he could look at the bronze serpent and live. The serpent was lifted up so that any who looked would live. But only those who looked upon it lived. And as Moses lifted up the serpent, even so was Jesus Christ lifted up that whoever believes would live.
Atonement is limited to the "whosoever believes" (e.g.,only those who looked upon the serpent lived), but Christ's death was also for the sins of all mankind (e.g., the bronze serpent was lifted up so that everyone who was bitten could look upon it). Christ died to so that all can be saved if they believe, but none of us believe (before I was saved I was lost). God works in the hearts of men (the elect) in such a way as to reveal the Truth of the gospel (they believe).