Noted military historian John Keegan takes a look at the question. The key paragraphs:
Could Iraq be the first civil war ever without battles, generals, explicit war aims, the use of partisan public rhetoric by civilian leaders, mass public participation and targets of a predominantly military nature? Even if Iraq today possessed these characteristics, it would still lack something even more important: the struggle for authority. In Iraq, the state actors are fighting for authority. But the others are not, which is probably why we do not hear from them. The Shia militias are the armed wings of the two biggest parties in parliament, and their people own the top ministries. Neither Badr nor the al-Sadr movement is big enough or strong enough to own the state itself. They balance each other while the Sunnis, whose violent actors are far smaller, provide the final guarantee against a full grab for power by either. It is no coincidence that the only player, apart from the state, that acknowledges war aims is the only player whose war aims constitute the traditional aspiration of exclusive control: the religious element of the Sunni insurgency. The aspiration to a new Baghdad caliphate frees the Wahhabis and Salafists from the pragmatic calculations of al-Sadr or the Baathists, and lets them dream of control, and talk about it on their websites.To me the words "civil war" seem to be thrown around with the carelessness of the word "quagmire" or shouted as part of a slogan like "no blood for oil" with the same amount of ignorance of the underlying facts of the matter.
Objectively, it must be concluded that the disorders in Iraq do not constitute a civil war but are nearer to a politico-military struggle for power. Such struggles in Muslim countries defy resolution because Islam is irreconcilably divided over the issue of the succession to Muhammad. It might be said that Islam is in a permanent state of civil war (at least where there is a significant minority of the opposing sect) and that authority in Muslim lands can be sustained only by repression if the state takes on a religious cast, since neither Shia nor Sunni communities can concede legitimacy to their opponents.
It seems to me that the phrase "nature abhors a vacuum" is the most apt to describe the violence in Iraq. There are small pockets where control is not secure and this power vacuum breeds the opportunity for violence as part of the grab for power. If the US and coalition forces were to "redeploy" from Iraq - that would create a tremendous vacuum at the top and this huge vacuum would cause a true civil war.
Thus it would be a self-fufilling prophesy. The people who say Iraq is in the midst of a civil war now and want us to pull the troops out would cause the civil war and mass bloodshed they imagine today by pulling the troops out.