The insurgents, beheaders, terrorist, and their broader Sunni supporters have to wage a PR guerilla war. Unable to defeat America militarily; they must drive us out in other ways. They have to make it too expensive for us, too dear in blood and treasure. But now they have a problem. George W. Bush is an irrational, "non reality-based," war-mongering, Crusader who ignores public opinion and thinks he has a direct line to God. That's a problem for them.
This is not to ignore, nor understate the problems of the government/occupation. Allawi and the Americans have to uphold their authority everywhere in Iraq. By definition, no city can be surrendered to the rebels, at least not permanently. Thus Fallujah. Thus Mosul. In every one of these cases, we must kill, capture, or dishearten as many insurgents as possible, fully aware that most survivors will slip away and fight again.
There is no simple way out. We must the resist the PR battle and win this one on the ground, one dead former Baathist or foreign fighter at a time. The Iraqi government and the US must make the price of insurgency too high for anyone to want to pay.