I know that statement is very much against the conventional wisdom, but it's also true. To prove it I'll look at what the worst-case scenario is and explain why even in this case the course of history is not ended.
The Islamo-fascists have thus far not seriously threatened our interests. None of their attacks have caused significant casualties or economic damage. 3000 people dead from 9/11 are significant from a psychological perspective but it would take many, many 9/11's to defeat us, and they haven't even managed to duplicate their feat over the past three years. The economic effects of 9/11 ended up being relatively minor as well, unsurprising for an economy as large and varied as the United States. The terrorists cannot possibly hope to defeat us materially using their current methods (other methods will be considered later). The only hope that they have is that their attacks would do enough damage psychologically for us to defeat ourselves. While many on the Left have tried to bring this about, there is no indication that we are in danger. Fortunately a majority of the American public has no desire to pull a Frenchie (i.e. surrender).
If the Islamo-fascists were able to get a "weapon of mass destruction" (i.e. nuclear, chemical or biological) then they would become much more of a threat. It would take a large amount of resources for them to actually defeat us even with these weapons. The destruction of even a city or two and a million people, as horrifying as that is, would not be enough; it would take a massive sustained campaign of terror. There also remain a number of tools that we have refrained from using in our fight. If we had to we could be much more aggressive, see the end of this article. The United States will NOT be defeated by terrorists, even if it requires the annihilation of all Muslims (though no one wants it to come to that). For all the hype about asymmetric threats, they do not change the fact that our overwhelming military superiority will protect us, even in the worst-case scenario.
If several U.S. cities were destroyed along with the Muslim world, history will still continue. Even a battered U.S. would remain the world's most powerful nation. Obviously there would be much more psychological damage, but we would not be defeated.
The bigger threat to our power is that another nation would become more powerful than us or at least powerful enough to challenge us (a la Soviet Union). That is why my examination of the trends in the relative power of the most important nations (started here) is still important. Even if our current "war on terror" goes spectacularly poorly it will not be our biggest ultimate threat.
Note: Because many say that the nation-state is becoming obsolete due to globalization (and thus the relative power of nations is unimportant) I will next discuss why the nation-state ain't goin' anywhere (at least for the foreseeable future).