From what I remember from Theology 101 (and if I can find my books I will get the actual quotes to you), while Adam and Eve are believed to represent the literal first humans, the narrative is what is written in figurative language. This is generally the same starting point in both Jewish and Christian circles.
Judaism, Catholicism, and Orthodoxy (along with most mainstream Protestants) concur that this is not a story about how sin was introduced into humanity as much as it is a story teaching that sin has been a factor in the human condition from the outset. The narrative simplifies this in an illustrative manner by giving the "first couple" a directive which they cannot fully complete without interference of the basic makeup of human nature.
Judaism sees this not as "original sin" but as describing a facet of humanity that does not disqualify anyone from being the same "very good" creation mentioned in Genesis 1. Humans aren't perfect because they were not created that way. In Judaism the thought is that humans need God and, unlike some in Christianity, the Jewish view is that God may equally need humans. We are two parts of puzzle, say many Jews of this story, both needing one another to be whole like the two lovers that later sing to one another in the Song of Solomon.
Christianity would understand this story in the light of the teachings of Jesus of Nazareth and Pauline teaching to the Gentiles. In Jewish theology God redeems the children of Abraham on the basis of a promise with a future but has not done this for humanity in general, nor fully fulfilled the Abrahamic covenant. The idea in Chrisitanity is that this facet of imperfection keeps redemption from being fully realized, and for them Jesus has come to remove it.
The narrative in Genesis 3 was in the light of this understanding labeled "original sin." It doesn't change the original view that the story is figurative, however. "Original sin" is the theological concept or interpretation of the event, but the first suggestions of this come from the written Gospels and Paul's letters. The term itself, being theological, does not occur directly in Scripture form.
The idea that this was a literal series of events was late in Christian history. The revivals in American religion which gave birth to Fundamentalism occurred among teachers who were generally not formally educated in theology. They have interpreted not merely the Biblical stories as literal for this reason but some of the theological discussions of the same as well. References to the imagery in Scripture and exegesis were seen as validating that the details were factual.
These groups often shared in the rejection of the universities of higher learning where these are generally learned (originally colleges came from Christian churches rejected by these new religious movements), and thus their hermeneutical views became absent of the traditions that carried the Biblical concepts to their generation.
It is from these groups that the Jehovah's Witnesses sprung, and they carried this "tradition-rejecting" tradition into their religion, claiming the events in Genesis have to be real.
One final word: the sacrifice of the cross is not a concept which Christianity claims to fully understand like the Witnesses. Christianity teaches that in some mysterious way the Cross is the Tree of Life promised to Adam and Eve (and obviously their children) in the original story. Though nailed to a dead tree, like the sacrifices that provided food for the Israelites at the Temple, this Tree provides the "true food" of the body and blood of Christ that gives life to anyone who "eats" from it. Where JWs see this a a sacrifice needed to appease a God who demands such a victim, Christianity sees it as God giving his life as "food" to share his life with humanity.