Some small minority of Sunnis in Iraq (those participating in the insurgency) are interested in starting a war against the Christians, Jews, Shia, Kurds, Non-relgious persons, etc. In this sense, I guess you could say that there is a civil war going on between the shia and the sunni. But here's the thing: the Shia alone are a majority of the population. When you combine them with the groups mentioned above AND the sunnis who are not interested in fighting, you don't have much of an opposition left. If by civil war you simply mean that Iraqis are killing other Iraqis, I would agree with you that Iraq is in a state of civil war. If, on the other hand, civil war is defined as a largescale military conflict between organized factions within a single nation, I would have to conclude that there is no civil war in Iraq.
Some people would undoubtedly like to see the emergence of a Sunni v. Shi'ite war, but that hasn't happened yet, as the group of radical Sunnis is small and will grow smaller as more people realize that the way to power is through elections, not IED's. These colors don't run (except in 1991
).
I also highly recommend you take a look at
this inside perspective on what is happening on Iraq. His conclusions are realistic, but relentlessly positive.