It's not like that. We've got both Sunni AND Shia on our side. The yearning for freedom doesn't know race, creed or gender.
At the same time, we've got revenge attacks by Iraqi Shia on Sunni, which were the ruling party under Saddam and the ever present Shia Iran continuously trying to take over Iraq, formerly controlled by Sunni Arabs, but now ANY Iraqi not on Iran's side is a target. THEN you have Sunni al Qaeda. THEN you have all those other blood clubs, like Hizbollah. All those groups are out for themselves. THEIR shared objective is the same: destroy Iraq's fledgeling democracy and achieve victory and dominion over the Great Satan and push Israel into the sea. With or without a new caliph depending on ideology.
"We've got both Sunni AND Shia on our side."
It's a good thing they're both on our side so we can crush the insurgency and put an end to this civil war, albeit a limited one. But the shiites and sadr army must be crushed as they are the main reason for this war going as far as it has so far.