David Ignatius pretty much nails it on the head:
...there's a lively debate within the military about just what accomplished the turnaround [in Iraq]. Was it numbers -- the five additional combat brigades? Was it the new counterinsurgency tactics Petraeus instilled among his troops? Or was it the brutally efficient new intelligence tools used by U.S. Special Operations forces to hunt and kill al-Qaeda in Iraq?
The answer, surely, is that it was a combination of all of the above. But the virtuous cycle that developed in Iraq would have been impossible without the signal of American resolve that President Bush sent in backing Petraeus and his strategy. Iraq was hurtling toward civil war in 2006 in part because Iraqis thought we were about to bail out; Petraeus and the surge changed that psychology.