Ultimately the US forces move to "Independant Kurdistan" to protect the Turks and Kurds from each other...and "guard" the oil fields... Because everyone knows the Kurds aren't going to stay in "New Iraq."
The Sunni and Shia will have a brief fight over parts of Baghdad...but it will be over and settled in about a month...with some ethnic cleansing done...the local "mullahs" will figure it out.
All police control will be local militia based... hence accepted by the local population.
The New Iraqi "national government" will exist only to cut the monthly checks for the oil money to the regional governments.
In twenty years or so...maybe the Shia and Sunni will opt for a more centralized government...but no army on earth will force them into it now...