Strategically, we need to look at the big picture. People fall into three categories: those who are sympathetic to us, those who fear us, and those who are hard core terrorists.
The sympathetic demographic is relatively unimportant.
The hard core terrorists are a tiny minority. They number in the thousands, and nothing we say or do will deter them from their mindless, murderous, faith-based initiative. The only way to deal with these people is to apprehend them or kill them in the process.
The demographic with the highest importance is the fearful one. There are at least a billion or more people who are unsympathetic to the United States because they fear American military intervention, and the abuse of American economic and political power. They may not like the terrorists, but they may see the terrorists as a reaction to a real threat, or as a counterbalance to American hegemony. The war in Iraq demonstrated to them that the US respected no one, and was willing to break all the rules in order to satiate its thirst for control.
This group, the fearful, is the real group we need to target. Not with bombs, but with candy and flowers, and with human rights and cultural respect. For every one-in-a-million of these US-fearing people we turn to terror, we create another thousand hard-core terrorists. If we fail to win hearts and minds among this demographic, we will LOSE!
Why does this fact elude the Bush administration? Bush has answered the question himself. He believes that this is an ideological war, and not a psychological one. For Bush, it's about looking and acting tough. About giving no quarter to active terrorists. He doesn't understand that direct counter-terrorism is a side-show that should play a lesser role in the public consciousness. This is why we're playing our cards so poorly that the fearful demographic has produced more terrorists than we have neutralized.
We cannot win when we cannot see the battlefield, and refuse to use effective weaponry. The only reason things aren't worse is that the other side isn't much better at this game than we are.
Update: Just 3 hours after I wrote this, If found this article at MSNBC:
Five years after 9/11, Arab resentment grows
"Even mainstream Arab professionals, like Jamil M'roue, who publishes and edits Beirut's English-language newspaper, the Daily Star, finds himself caught up in the contradiction of both being appalled by the terror of 9/11 and of applauding al-Qaida when, as he puts it, it gets to the “rabid tiger” that America has become."