You may be giving the American public at large too much credit. After the major military action is over and the news coming out of Iraq has become more routine America will revert to old habits.
Most Americans give the news very little attention. (Thats where the big media got the If it bleeds it leads philosophy.) If it doesnt immediately grab their attention the greater public switches channels to ESPN or a Soap. Watching more than one hour of news a day (probably less) is totally out of the question.
If the major news media can get some poor little pathetic bandaged child and its mother on tape wailing, then by hook or crook blame it on the Allied military action, they will sway many against the occupation.