Kissinger's hypothesis is based on the lack of an Iraqi national identity which unites them. The bulk of Iraqis actually have much in common which unites them as a nation of which the following is just one example:
What the Iraqis lack is a combination of lack of security and lack of will to take charge of their own personal destiny. Someone gets shot in the street, and the reaction is to avoid getting involved and expect the Americans to do all the hard work for them. This attitude was ingrained by long term rule by Saddam and his secret police. The continuation of this attitude is what the extremist minority takes advantage of to dominate the masses. What will work is the continued training and refinement of the Iraqi security forces. As expected, the quick build up of the security forces resulted in a less than ideal force which is expectedly Shiite heavy. The current government, led by Maliki, also reflects the Shiite influence especially of those of the extremists under Sadr. We will have to leave the government correction and refinement up to the Iraqi people. It won't be a quick process and may take decades to get right, but there are many examples of shaky imperfect democracies that eventually shake off their mistakes. All we can do is build up the Iraqi security forces and do the best we can to prevent those forces being used for the wrong reasons.
And yes, we've done this before. South Korea is a prime example for which I am personally familiar with. It was a country totally devastated by the Korean War. The "democracy" that was set up was severely flawed, and the South Korean security forces set up by the USA was just used to repress the people and make those unjustly accused to "disappear". There was even rampant insurgency supported by an enemy neighbor, North Korea. It took decades, but democracy became real in more than just name, and South Korea is now one of the USA's most important economic and political partners in the far east. This is possible for Iraq as well, but don't expect it to occur quickly or cleanly.