This is a most selfish saying that we may find in the most popular segments of Christianity.
The idea and confidence with this belief is that Jesus' death is good enough that there is no more death needed for salvation. It is like saying: "Jesus suffered for me and so I don't suffer any more." That is what Mel Gibson's movie THE PASSION OF THE CHRIST tries to convey to people without asking the ugliness of evil and violence done on to Jesus.
Most critically and candidly speaking, Jesus did not come to die; rather, his death is a result of what he said and did for the kingdom of God (better to say "God's rule of peace, justice, and mercy").
Paul says that "Jesus was crucified by weakness (eks astheneias)" (2 Cor 13:4a). The often translation of Jesus' Crucifixion "in weakness" does not seem to convey the intended meaning by Paul, who acknowledges Jesus' weakness (not acting like weak, but he was weak and could not overcome violence).
Jesus looked like he failed. But God makes him alive (2 Cor 13:4b). It is God who raised him and made him alive now. The true form of religion is based on other-centered life and sacrifice; the rest is up to God.
In light of the above, I am concerned that Jesus is being misrepresented in popular circles of Christianity today. How can we separate Jesus' death from ours? Jesus died, so do we.