As for the question on whether were fighting insurgents or doing some sort of quazi peace enforcement between multiple warring sides can be debated indefinitely, and everyone's argument would have a grain of truth, which is the essence of our challenge in Iraq, we don't even understand the nature of the problem, which means any strategy is at best an educated guess on how to best respond.
Excellent point Global Scout. I've held the exact same view for too long. The problem is too complex, too multi-faceted to be totally grasped by 1 or 100, which make administration and execution of a strategy very hard. Let's just call them bad guys, kill them or make them realize their path is pointless, and negotiate with the non-so bad ones.

I know in some cases were fighting a resistance and we're the occuppying foreign power. There is no other way to define it, no matter how unplatable this is to our American tastes. There is also an internal resistance against the Iraqi government from various Sunni groups, and perhaps some the Shi'a groups vying for power, so there is an insurgency. There is a war below the government level between Shi'a and Sunni, and always tension between Kurd and Arab, so there is civil conflict. Then there are foregin fighters on all sides, but AQI being the best known the most dangerous, who have the potential of changing the nature of the conflict into something else if we're not careful.
This is another excellent point that I have tried to articulate here before, but failed I suppose. We need to stop getting hung up on definitions and terms, because nothing in Iraq or Afghanistan is black and white. There is too much gray area, either outside the FOB walls, after the patrol has left, etc., that we cannot see. Unfortunately, the inclination to package Iraq with a set box of terms hurts us all, especially the administration and it's advisors. We may know generally what is going on...and can analyze COIN metrics to make an assesment of what phase or stage we may have transitioned to, but it appears we get burned often because the situation shifts ever so subtly and we didn't catch it. Or things go kinetic very quickly, like the Samarra Mosque bombing, and we aren't in a position to affect much.

To put some of what I'm trying to say in perspective, how much would the coalition be able to influence the situation on the ground in the following scenarios (because I believe unrestrained Sunni-Shi'a violence would ensue):

-Sistani is assasinated. By which side does not matter, b/c the blame will always fall on the Sunni/AQ.

-Sadr is somehow assasinated and that too points back to the Sunni.

-Another shrine is attacked and destroyed.

Sistani and/or Sadr represent the most dangerous situations methinks, but in all seriousness, what are we capable of doing if either of those two meet a nefarious demise?