The only reason that we have a question is because the Bush administration will not admit that they failed.  Because a civil war has to be seen as a failure.  NPR had a story on this today.  NYT had a story also.  Randi Rhodes talked about it.  NBC and the LA Times have agreed to call Iraq a civil war. 

James Fearon, Professor of Political Science from Stanford, has a few words of wisdom on this subject:

Does the conflict in Iraq amount to a civil war? In many ways, the public debate over this question is largely political. Calling Iraq a "civil war" implies yet another failure for the Bush administration and adds force to the question of whether U.S. troops still have a constructive role to play.

Politics aside, however, the definition of civil war is not arbitrary. For some -- and perhaps especially Americans -- the term brings to mind all-out historical conflicts along the lines of the U.S. or Spanish civil wars. According to this notion, there will not be civil war in Iraq until we see mass mobilization of sectarian communities behind more or less conventional armies.

But a more standard definition is common today:

1) Civil war refers to a violent conflict between organized groups within a country that are fighting over control of the government, one side's separatist goals, or some divisive government policy.  more

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Added the video below.