Who would they have declared war on? Iraq. We beat them. Many to most of the so called "insurgents" are foreign fighters. The nature of guerrilla warfare is that small numbers of unconventional forces can tie down large numbers of conventional forces.
Only if we are willing to go after the sources, be they in Saudi Arabia, Iran or Syria (plus Lebanon and the Palestinian territories) of the terrorists. That includes their sources of funding.
We, as a country, do not have the stones for that, even though our military could do it.
We might be a lot further down the road if we had taken a hardline with alSadr from day one before built his militia and consolidated his power base and been allowed to join the government...also, taken the advice in the very beginning and split into three quadrants instead of letting Turkey call the shots on that because of their dislike of the Kurds -- the only group with it's act together in Iraq.