Actually, I don't think we should, yet, but probably not for the reason you think.
America has a bunch of energy sources, just none that are either economically or politically cheap enough to use. Yet. Coal, oil, natural gas, oil shale, etc. It's all there, just too expensive when easy oil is readily available.
Think of all that as our retirement plan. <img src="/images/graemlins/smile.gif" alt="" /> Let's run the rest of the world out of oil, then sell our slightly dirtyier, slightly harder to extract energy back to them at 2x what we paid for theirs. <img src="/images/graemlins/smile.gif" alt="" /> <img src="/images/graemlins/smile.gif" alt="" />
If we start drilling now, we'd be tempted to use it too soon for this to work. When do we do it? When either the middle east is buying oil from somewhere else, or have switched over to something other than oil (completely). Till then, bank it.