The New York Times reports that the seige of Fallujah seems to be giving Iyad Allawi a case of political leprosy: nobody else in Iraq wants to touch him. Insfoar as the elections to come are in some sense genuinely democratic, that will be a problem for him, and for the United States as his main backer.
However, under conditions of martial law, it seems unlikely that mere unpopularity will prevent Allawi from staying in power.