The real sticking point, for me, regarding heaven and eternal life is the concept of "the soul". While thoughts on the soul differ widely, it seems to me that the most popular notion remains "the ghost in the machine" model, in which the soul (or spirit) is viewed as a quasi-physical entity that leaves the body upon death. This concept of the soul makes me uncomfortable, primarily because it reminds me too much of the Gnostic "spark of divinity", which has a lot in common with New Age nonsense.
The soul is also problematic scientifically, since it assumes a mind/body dualism that simply doesn't exist. As J.C. Polkinghorne, a physicist and Anglican priest, writes in Science and Theology, science views humans as psychosomatic entities; that is, as animated bodies and not incarnated souls. Incidentally, "this was the way in which the ancient Hebrews seem to have conceived of humanity, and a psychosomatic account of human nature is the dominant, but not exclusive, way of thinking to be found in the Bible." In other words, the concept of the soul is more Hellenistic than biblical.
But if the soul doesn't exist, than what part of us survives death? Instead of souls, Polkinghorne prefers to speak of the self, which "is composed of the immensely complex 'pattern' in which our matter is organized." He goes on to say:
"It seems a coherent belief that God will remember and reconstitute the pattern that is a human being, in an act of resurrection taking place beyond present history. Thus the Christian hope centers on a real death followed by a real resurrection, brought about through the power and merciful faithfulness of God. Christianity is not concerned with a claim that there is human survival because there is an intrinsically immortal, purely spiritual, part in our being. The ground of hope for a destiny beyond death does not lie in human nature at all, but in divine love."
So to be faithful to both the Bible and science, we should abandon all notions of the immortality of the soul, and focus our Christian hope on the resurrection of the dead. But where does this leave heaven? Should it be downplayed or eliminated in Christian thinking? I'm not sure, but it's an interesting question to ponder...