The UN currently estimates about 100 civilian deaths per day in Iraq. To compare, there were roughly 190 civilian deaths per day during the American civil war, with the key caveat that the majority of those were from disease rather than violence, which is definitely not the case in Iraq.
The Los Angeles Times has apparently already made the policy decision to refer to the fighting in Iraq as a civil war. One speaker I heard today made the case for referring to it as a civil war, with the hope that this will drive the international community to take measures that have been used in other civil war situations, such as Sri Lanka. As long as the United States is making Iraq largely our backyard, however, I think this is unlikely.