Occupying a conquered country and converting it from a dictatorship to a democracy is something the U.S. has done before. Germany and Japan both were occupied by U.S. and allied forces for some seven years after World War II. But there are considerable differences between the two nations and Iraq. Some good, some not so good. Japan and Germany had homogenous and law abiding populations, Iraq comprises some 150 tribes, divided by religion (Sunni and Shia Islam) and ethnicity (Arabs and Kurds). The nation we know of as Iraq has only existed since the 1920s. Before that, it was several regions that belonged to one empire or another for thousands of years.
The U.S. Army paramilitary occupation forces used in Japan and Germany were small for the size of the population. For example, Japan in 1945 had a population nearly four times that of Iraq today. The average number of U.S. occupation troops in Japan were 110,000.
Japan or Germany had several generations of experience with a parliament, so most people knew what democracy was and also knew that dictators had brought nothing but grief. Same situation in Iraq, where there has been a parliament for many years, but also a king or dictator who could ignore (or replace) anything the parliament wanted.
Based on the Japanese experience, it would appear that a paramilitary occupation force of 30-40,000 would be required for Iraq. Since the Special Forces have been studying the post World War II occupations for over half a century, they have come up with a lot of new ideas to expedite the process. However, they will face one major problem that was not found in post-World War II Germany or Japan; rampant corruption and factionalism. This is a major problem throughout the Arab world, and the Third World in general. Thus the occupation of Iraq would be a major social experiment in trying to establish an honest, efficient civil society in a country that have never experienced that form of government. There no reason to believe such a transformation is impossible. Millions of people have come from Iraq, and countries like Iraq, to America and easily adapted to a democratic society.
But what's all this going to cost? First, you have to realize that there's a certain amount of dishonesty in the numbers government's put out about the cost of peacekeeping operations. The U.S. says it costs over $400,000 a year for each peacekeeper it has in Bosnia, while Germany says it only costs them $37,000 a year per man in the Balkans. The UN pays some $75,000 per year per soldier for peacekeeping operations all over the world. Are all these people from the same planet? Yes, but not everyone keeps the books the same way. The Germans are only counting additional costs, above what they would be spending if their troops stayed in Germany and did that they normally do (train, and turn out for the occasional natural disaster.) The UN has to hire peacekeepers, usually from Third World nations (where labor costs are much lower), and supply them with food, shelter, transportation and medical care while they are off in some troubled part of the world. That said, the U.S. does treat it's peacekeeping troops to a lavish lifestyle (compared to other European troops), once they have been in some place for a year or so. This is expensive. For example, in Kosovo, some 5,000 U.S. troops (and some civilians) live in a camp that cost $350 million to build (in 1999), and $50 million a year to maintain. The comfy quarters are actually necessary because it has become customary to forbid U.S. troops to mix with the locals or have alcohol on base. Lacking easy access to booze or sex, the two most popular recreational activities for soldiers away from home, the splendidly equipped camps attempt to make up for it. Naturally, when the bean counters are calculating what it costs to maintain U.S. peacekeepers in a place like Kosovo, the costs of building and maintaining well equipped bases is taken into account. But if operated like the other European armies (allowing the troops to date and drink), you could put them up in less expensive digs. The European peacekeepers don't appear to be suffering from deprivation, or failure to get the job done, because of their less expensive operating costs.
But even if the occupation troops in Iraq were put up as lavishly as those in Kosovo, the U.S. wouldn't have to pay for it. While post World War II Japan and Germany were broke (and heavily bombed). Iraq has all that oil money. Bases could be built for American peacekeepers, that would eventually be turned over to the Iraqi army. Indeed, all the American troops would have to do is rebuild existing Iraqi army bases (which is what was often done in Japan and Germany). The Iraqis aren't going to be complaining. After three decades of Saddam and his wars, which kept most Iraqis poor, they are going to see a sharp increase in their standard of living. Honest cops and government officials will be another welcome novelty, as will the arrest and trail of those officials who just couldn't shake their bad old habits. With the Iraqis paying for housing, fuel (they have plenty of that) and some other costs, the actual cost, for the U.S., of the occupation force, would be about a billion dollars a year.
The biggest problem in Iraq would be dealing with demands from many Iraqis for justice. Hundreds of thousands of Iraqis have been jailed, tortured or killed by Saddams secret police, and their family's have not forgotten. Once there is a free press, questions will be asked, and the occupation government will have to deal with it. This is the great unknown, not the cost of peacekeepers. But other nations have dealt with this sort of thing in the past decade, and so can Iraq. All the Iraqis need is a chance.
Given the past performance of the Iraqi army, and especially after the beating they got in 1991, there's little doubt that the U.S. could quickly conquer the country. A show of force and some psychological warfare would get even the Republican Guard to lay down their arms (the alternative being death.) Then what?