After the bombing, from February of 2006 until the end of 2006, the Shiites death squads (with the tacit help of the Iraqi military) went to work against the Sunnis in Baghdad and its suburbs. In attacking the Sunnis and winning the Battle for Baghdad, the Shiites proved to the Sunnis that they could defeat them quite easily if need be. That fact broke the Sunnis' will to fight because they had always thought that if they just outlasted us, they would easily be able to take over Iraq and run it like they had before our troops invaded. Once the Sunnis' belief in the submsiveness of the Shiites was shattered, the Sunnis stopped fighting us and instead sought our help in protecting them from the Shiites.
The problem in Iraq was that we could never win the fight against the Sunnis - only the Shiites could do that. As such, it was the awakening of the Shiite giant in Iraq is which lead directly to the Sunnis Awakening and, more importantly, to the evisceration of the Sunni belief in their own invincibility.
More correctly, I should say that our troops could never defeat Sunni fantasies about regaining the dominant position in Iraq - only the Shiites could defeat those fantasies.