To give you an idea of just how much Iraq needed our significant presence to hold off the forces trying to tear apart Iraq, consider that while the Shia-dominated government of Iraq fears that a successful Sunni revolt against Assad in Syria would inspire Iraq's Sunni Arabs to revolt again; in the years prior to the revolt, Assad's Shia-like Alawite government funneled in Sunni Arab suicide bombers to help the jihadis attack Iraq's Shias; and prior to the downfall of Saddam Hussein, Syria funneled in Sunni Arab jihadis to fill out Saddam's Fedayeen bully boy outfit that was used to whip the Iraqi Shias into line.
When it just doesn't matter what faction of Islam runs Syria for it to be a threat to Iraq, you have to be careful about how much you settle on the Shia-Sunni divide as the root cause of Iraq's problems.