I was having trouble explaining how God was more than intuition for me. But thinking on it, I think I have a better analogy. Prove love exists. It's something we feel, something we do, something we trust in, something we will give up anything for. For me, God is the same. I can feel it. I simply know its there. I see evidence of it everywhere. In things that can be explained by other things, but don't preclude God either.
Oh, and I had another thought. (I know, like two in a row!) If atheists weren't so mocking and condescending, people of faith might be a lot more willing to work with them on issues of separation of church and state. It seems to me that if someone is an atheist and wants to get a total separation of the two, that should matter a hell of a lot more than trying to convince me that God doesn't exist. The first is negotiable, the second isn't. Also, if you wonder why some Christians have a hard time with the idea of removing God from the classroom, government, etc., realize that militant atheism in the form of mocking condescension is part of the reason. We really don't want that to become normal. But if we were shown some respect for our beliefs and shown that no, we won't be subject to scorn and ridicule from an atheistic government, then we probably would be a lot more willing to give up the power. At least some of us. Other people just hang on to power for the sake of having it. And frankly, that's not limited to Christians.