The government is installed there CAUSED this latest problem by simply being the Shia version of Saddam Hussein.
During the 2008 Presidential debates there was only one voice that made a lick of sense to me and that was Joe Biden. He simply observed that the West has arbitrarily created the boundaries of Iraq, forcing together three completely different cultures. The Sunni, Shia and Kurds have lived in neighboring areas for a long time more-or-less peacefully. Forcing them all to live under one winner-take-all government was never going to be stable, unless you have a ruthless dictator that meets the slightest instability with executions.
Biden said that the best solution would be to form three nations, or at least a government structure that recognized three mostly autonomous states.
Joe was right, and he still seems to be the only person who has figured this out. And that ought to be the baseline requirement for any assistance from the West.