Oh, FFS.
The Sunni bloc is quitting Maliki's government because they feel they're being shut out of important processes, especially security. That means Maliki is going soft on partisan militias infiltrating the official state military. Which he's doing because Dawa, SCIRI (or whatever they're being called now), and Al-Sadr's bloc are all part of his coalition.
As fucked up as this is, it's actually how a parliamentary democracy is meant to work. If no one party has a majority, they stitch together a coalition. The biggest bloc (in this case the UIA) primarily sets the agenda, but has to make concessions to its partners. A group with a large minority stake wanted concessions that parts of the majority were unwilling to give it.
The part where it falls apart is that in a functioning democracy, a new coalition would be formed, and the most pressing issues would be settled legislatively, if by thin margins.
That won't happen here, because it relies on politicians feeling pressure from the electorate, and seeing the parliament as the only way to advance their agenda, or acquire power. In Iraq, there's almost no functioning civil society, and security forces are split among local tribal forces, religious/partisan militias, a weak state army that's heavily infiltrated by those militias, and an occupying foreign army with lots of firepower but that doesn't speak the language much.
I'm sure that 99% of the Iraqi parliament would want peace, in a general sense. A vast majority would probably be willing to compromise on important issues if they thought that would actually bring peace.
The problem is that for any individual politician or party, there is no guarantee that compromising, or even playing by the rules, will pay off. You need mutual trust, where each side thinks it can put down its gun for a moment without the other side pressing the advantage and shooting them in the face.
Right now, there are big incentives to work outside the government (read: violence) to create more favorable conditions for whatever your side in the civil war is, and hold off on a political solution until the facts on the ground make your victory inevitable. That's why the Kurds kept stalling on a census of Kirkuk as the PKK evicted Arabs and brought in Kurdish residents by the truckload.
Maybe if enough Iraqis wanted peace, then a new, dovish grassroots movement would replace the current politicians, right? Except that's next to impossible, because IRAQ HAS NO CIVIL SOCIETY, AND LOCAL AND REGIONAL SECURITY IS DEPENDENT UPON PARTISAN MILITIAS.
