An Open Letter to Paul Bremer Giving Advice Based on Civ 3

First, quell the resisters! Install a military force with strong units such as the Knight, Pikeman, or Hoplite. If you have not created a Barracks in Baghdad, I suggest doing that, too. Subsequent military units built there will begin as Veterans. (We don't want Regular Swordsmen going into Tikrit, do we? I didn't think so.) Obviously you should Fortify (Ctrl-F) your forces if you haven't done so already.

Secondly, because the U.S. is a Democracy (or Republic maybe), the number of happy citizens is going to be greatly reduced when you're fighting a drawn out foreign war. From experience, I would suggest switching back to Despotism for a few turns (years). People under Despotism are less likely to be upset about war.