It's actually the basis of Christianity as well, hence the need for a messiah. The curse of Adam (original sin) that required sacrifice to God was to be expiated by the messiah (who would be the final sacrifice). Without the sin of Adam being passed down to his offspring (much like the sin of Cain passed down to make his offspring monstrous, a common belief in both Jewish and early Christian traditions), man would have the potential to be sinless. Early Christian doctrine (as it was based on the Jewish messianic tradition) was clear on the sinful nature of man from birth (enshrined in early Catholicism as the doctrine of original sin). It wasn't until the Protestant Reformation that some Christian denominations began to "reinterpret" the idea of the sins of the fathers being visited on the sons. Medieval literature (my particular specialty) was almost universally in agreement as to this transference, and you see it alluded to in many secular contexts as well (even to the point that Malory's Arthur must suffer for the sins of Uther... through Morgana and Mordred).
Many early Christians (and, ironically Jews as well) would have argued that without Adam's sin (for which we still suffer), Christ is not needed...
Calvinists still believe in the total depravity of man from birth. He is so depraved, he cannot come to God by himself. God must come to him (Election)