Cheney is not the first to make that comparison. It is a tempting comparison, because there is no more recent example of a country that had so much power for such a long period of time. If history is any guide, the U.S. will eventually lose out to someone else, but it is not clear who that would be. The Chinese would be a possibility, but at the moment they have a lot of catching up to do.
Predicting the future is a tricky business. What impact will diminished resources or global warming have? Are we heading toward better times or global dystopia? Is world government a possibility? I would not hazard a guess about any of this.