Dear Paul Bremer,
I feel your pain. I, too, have tried to topple dictators, usurp power, and occupy foreign nations while trying to steel domestic support for military intervention. It is not easy, to be sure. Herewith I present a synthesis of lessons I learned as a fierce global power (in Civilization 3, Game of the Year Edition, by MacSoft/Atari). Perhaps you will discover something helpful for the U.S. occupation of Iraq.
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. The biggest roadblock here is the interim Anarchy period, but my Domestic Advisors (F1) have always told me to ride it out. They were always right. You can switch back to Democracy or Monarchy (or whatever you want!) later.
Next, it is important to produce some Workers and get those railroads built! Moving resources and people through your recently toppled region is essential. What is especially crucial is to build infrastructure around natural resources (in my case, Iron, Spices, and Dyes; in your case oil I guess). Once you bring these resources into the city residents will be happier. I bet those Iraqis will be real happy to see U.S. tankers and pipes snatching up all that oil!
Hopefully, all will be better soon. Once you’ve made Iraq yours, who knows how wide America’s high culture will spread. Ideally our regional influence will increase, our boundaries will grow, and other cities (e.g., Tehran, Damascus) will depose their mayors and swear allegiance to the U.S. Best of luck! Remember: next time start on Chieftain—it’s way easier!