It depends on your definition of close...

Is it possible to be too close to God? It depends on your definition of close. I can be close to someone on an elevator because it's crowded and we continue to bump shoulders. I can be so close that I have to pardon myself politely before squeezing out of the open door. That's proximity. I can be close to someone without knowing who he is. I can also be close to someone who is miles away because our lives, our heart, our stories are intimately connected. My best friend can live in another state and still be my closest friend.

If your view of closeness to God centers on a relationship of obedience and reverence, then by all means, get as close as you can. If your definition of closeness is proximity, tread lightly. He is the creator God of the universe who occupies a space and a realm we cannot begin to touch. There is a way to approach God and it is not casual or light. Through Christ, we have access to God's mighty throne of grace, but it is still a throne and should be treated as such.