The unspoken reason for many Gulf states opposing the overthrowing Saddam Hussein is not any love for the current Iraqi government, but fear of what a democratically elected Iraqi government would do for their ability to control the Shiite minorities. Over sixty percent of Iraqis are Shias, and a fairly elected Iraqi government would be dominated by Shias. All the Arab Persian Gulf states have Shia minorities, and these minorities have been dumped on for centuries. If Iraq were run by Shias, the other Gulf states would have to deal with Shia minorities who could now call on overt, or covert, support from their "Shia brothers" in Iraq.
Shia Islam spilt off from Sunni Islam over a thousand years ago, and many Sunnis consider Shias heretics. This is what is preached openly in Saudi Arabia (although the government officially objects to this sort of thing, they won't take strong measures to stop it.) In practice, Shias are about as different from Sunnis as Roman Catholics are from Protestants. Shias are allowed to go on a Hadj pilgrimage to Mecca, but usually in separate groups, and with occasional violence between Shias and Sunnis. In Pakistan, Shia and Sunni extremists have been bombing and shooting each other for years. Iran is dominated by Shia clergy, many of whom openly call for administering a little attitude adjustment to Sunnis.
Iraq also contains the most holy shrines of Shia Islam, making a Shia run Iraq a natural center for those interested in obtaining justice for Shias throughout the Middle East (Syria and Lebanon also have Shia minorities.) When the Turks conquered the area that is now Iraq in the 16th century, they pushed out the Shia Iranians, removed Shia Arabs from the government and put the local Sunni Arab minority in charge. That has been the situation ever since, and Saddam is seen as another in a long line of Sunni tyrants who illegitimately rule the local Shia majority.
This situation has given rise to fears that the overthrow of Saddam would lead to anarchy and civil war. During the 1991 Shia uprising, Sunni officials and their families were killed in great numbers in southern Iraq. But it only became a major fight when the Sunni Republican Guard moved in and killed thousands of Shias. If Saddam's government is overthrown, the Republican Guard will no longer exist. While a lot of Sunnis in southern Iraq would flee north, there wouldn't be a civil war. It's also important to remember that the Iraqis are in no mood for more war. They have suffered under two decades of Saddam's bloody rule and are well aware of the fifteen year (1975-90) civil war in Lebanon (which is 40 percent Shiite), a war that accomplished nothing and left the most prosperous non-oil Islamic state in the Middle East in ruins. The Iraqi Shias are more interested in running their own affairs, and getting a fair share of the oil money, than in starting a civil war.
The most important thing for most Iraqis is family income and economic security. Saddam has used a nationwide rationing system to control the population, punishing any group seen as disloyal by cutting off food and other goods. A post Saddam government would have to use, at first, many of the people current running Saddam's food distribution system. Iraq has a large government bureaucracy, employing over ten percent of the work force. While the secret police and Republican Guard can be dispensed with, that still leaves nearly a million government employees. Loyalty to Saddam has always been a requirement for government employees, and the Shias will want more of those jobs going to those who long opposed Saddam. Eventually, there will have to be reforms in the Iraqi civil service.
Running a conquered nation is nothing new. It's been done often in the last century, and been done effectively. But it requires a lot of people and is expensive. Even though Iraq has huge oil wealth, twelve years of embargo have left the oil fields and pipelines run down and in need of massive maintenance. Doing this will provide jobs for Iraqis, but it will take billions of dollars in loans to Iraq to finance it.
For the Shias, and all other Iraqis, it's all about money and jobs, as well as freedom from tyranny.
China is reducing it's embassy staff and warning Chinese citizens to leave the country because of the possibility of war.