I knew that. I wasn't making a presentation in a political science class. My reference is how U.S. leaders and statesmen constantly use the label of "world's greatest democracy" when describing the American culture as opposed to the mechanics of governance. I could just as comfortably used the label oligarchy, plutocracy, or kleptocracy.
At the end of the day we are a nation of, by, and for the people - call it democracy or mobocracy. However, as long as you have the constitutional component in whatever you want to call our system, than it's more likely than not that extreme views and policies will be held in check. Sure, I suppose a majority could vote to suspend the constitution in part or whole, but that's highly unlikely because it would not serve their self-interests in the long run, as you noted the risk of falling out of majority. It's not the republic that protects all rights, but the constitution.