Thinking of the words of Jesus - he was able to do things like heal people, say the exact words someone needed to hear, feel compassion for those who aggravated him from ignorance or deliberately, 'conjure' money from a fish's mouth (or at least know the fish had just gulped a coin). And he said we will be able to do much more than he ever did because he didn't have a long life.
I've heard often that thinking we can do anything is wrong, that it all depends on the Father. Like scripture says, without me you can do nothing. (Is that without Jesus?) Anyway, I believe that but I see that it's because we've been made with these capabilities in the first place. I think He made us that way. Perhaps the spirit in us is what gives us access to what we are able to do. Otherwise, we stop ourselves, sabotage ourselves. Or He stops us. Seems anyone can do awesome things; maybe they are valueless without the right purpose. There's a blog I've been reading, Brain Stimulant, very interesting but at times disturbing. Do we really want to give control of our moods, our intelligence, our very souls it seems, to doctors and pharmaceutical companies?
I'm not sure that acknowledging what is in us, what we can achieve on our own is denying the power of God. He created humans in the first place, however it was done, we were made this way.
What I do know of God is that HE IS. It's like everything that is - He's there. Scripture says man is without excuse because nature declares His glory. Sometimes that's hard to see in people, in animals, in nature. Is it that we have fouled ourselves and the planet? That sounds totally disgusting. But can we still see the awesomeness and the potential - the way things are intended to be if we only look for it?