I think the answer can be found in Iran, Iraq's nextdoor neighbour. After the Second World War, Iran's legitimate government began to attempt Iranian nationalism, seeking to stop its oil being exploited by foreign companies. As a result, the American government interfered, and overthrew the government (or at least assisted), apponting the Shah once more, who was suitably pro-US. So the US deliberately overthrew a legitimate government to impose a non-democratic dictator. Of course, the result was Iranian revolution in 1979, and a country that isn't too friendly towards the West. In fact, Bush referred to Iran as being 'evil' last year.
So, what will happen? The US clearly wants at least relations with the new Iraq, if not influence - in twenty years time will we once again be saying 'Oops! They could have handled that better!'?