Many atheists seem to dismiss the belief in the "supernatural". Is the word supernatural in the Bible? Are Christians making assumptions, or portraying God in a way that is non-Biblical. I probably haven’t thought about this much, but saying "supernatural" means saying "magic" or "impossible" to a non-Believer. How can we explain this to a non-Believer without diminishing God to a theory, or a law. Also "omnipotent" seems to be problematic. Can an omnipotent God make a rock that is so large that he cannot move it? How can we define God without making claims that are too preposterous for a non-believer?
I completely agree with you that many atheists dismiss the idea of the supernatural by simply assuming it does not exist. This is a circular reasoning which is of no value in answering the question of whether supernatural things happen. It is hard to arrive at a definition of supernatural which all will accept. In my newest book (written with David Eastman, available at www.ipibooks.com), we define a miracle as a supernatural event. A supernatural event is an event which, according to the laws of nature, "cannot" happen. For example, when Jesus turned water to wine, that clearly is not "possible" according to the laws of nature which we can discover by experiment. Hydrogen and oxygen atoms do not change to carbon and nitrogen atoms (required for water to be changed to wine). The word supernatural is not in the Bible because it is in Greek, not English. A better question is whether the idea supernatural is expressed by any word or idea in the Greek New Testament. The answer is yes. The New Testament uses the Greek words which are equivalent to "sign," "wonder," and "miracle." All of these can be thought to be equivalent to supernatural. There is more discussion of this in the book I already mentioned.
No, in general Christians are not misportraying the Bible or God when they use the phrase supernatural to describe the miracles worked by Jesus. Supernatural is NOT the same as magical. Given that Jesus worked miralcles, apparently supernatural is not "impossible," despite the claims of atheists. As I already said, their argument against the supernatural is circular and of no value. I believe the evidence for the miracles of Jesus is very strong. To be completely honest, I do not have a very good working definition of the word magic. Sometimes the word means trickery and sometimes it means satanic-inspired miracles and sometimes I don’t know exactly what it is (like in Exodus when the magicians in Pharoah’s court worked magic).
How to best explain this to non-believers depends on the particular preconceptions of the individual people. Let me give a generic suggestion. We should first point out that the naturalists argument against miracles is circular and really does not help answer the question. One cannot disprove the miracles of Jesus by simply declaring them not possible. Then I would pass on to present the really quite overwhelming evidence that Jesus did in fact work miracles. Again, the book I mention above can be helpful for you there.
It is my experience that few people who are fair minded struggle with the idea of omnipotence. Such tricks as trying to disprove the omnipotence of God by saying he cannot make a rock he cannot lift is only useful to those who are trying to avoid the question. I am not saying that it is a simple question, but my experience is that most people have a kind of intuitive concept of what we mean when we say God is omnipotent. You can define God as Creator of the Universe. You can define God as the ultimate Cause of things. Of course, God is more complicated than that, and you can use the Bible to flesh out these definitions, but that can get you started with a non-believer.
Hope this helps.