How can we solve the political differences in Iraq?

I don't know. Maybe the same way we do here?

The suggestion is that American forces must keep fighting in Iraq until the Arabs and Kurds have put aside their differences, resolved their internal tensions, and started singing "kumbaya" in Arabic. But even the president's most ambitious aims involved only establishing a stable and peaceful democracy in Iraq--which is very different from resolving all tensions, as anyone who knows anything about democracy can tell you. For the United States, reconciliation should mean persuading the peoples of Iraq to address their problems and power struggles peacefully, through a political process rather than through violence, and to reject and oppose those who seek to use force to gain leverage in the political process. That is exactly what we are now in the midst of doing.

h/t BigDog