JW, I just think you're wrong on this.
The entire world will be cheering when the US is defeated in Iraq. Al Queda will make enormous hay out of this. This will be far more important to Islamist extremism throughout the world than 9/11 ever was.
On one hand, we can do ourselves a disfavor by lumping all enemies into one big monolithic Muslim Enemy and therefore not smartly allow them to work against each other.
But on the other hand, it misses the enormous point of what the Islamists represent throughout Islam. First let me state the obvious: no, not all Muslims are terrorists. Not all Muslims are fanatics. Most are decent and just want to get on with their lives. But...drum roll please...most all Muslims at the very least can't help but sort of admire these crazy bastards.
Remember, the average Muslim finds Western and particularly US culture repulsive, vile, even evil and dangerous. They are frightened by it. They hate it. They don't want it to corrupt their own. The average, non-violent, decent, normal Muslim sees American children with their own porn pages, zero respect for any kind of authority, a race to the bottom in every social indicator, the fact that we celebrate Britney Spears and her not wearing panties as she steps out of a limo...
This is worse than Saddam to them. They would far more prefer a dictator than what they consider Western moral depravity. And then they realize that all of the Arab strong men are in fact corrupt and held up by the West, or else are corrupt and at odds with the West but basically toothless. And don't forget Arabs feel deeply wounded by history.
So all Muslims, let alone extremists, see a pack of Arabs and Muslims of all types, be it Al Queda, Sunni, Shiite, it doesn't really matter, and it is a boon to all extremists.