Everything you wanted to know, but were afraid to ask.
The U.S. government in Washington has never fully understood the Sunni ' Shia divide which is akin to the Catholic'Protestant divide that led to centuries of war and strife in the Christian world, even as recent as the troubles in Ireland.
Iran is Shia and Saudi Arabia is Sunni. Iraq and Syria are mixed and that's the basis of the fighting today. Saddam Hussain was a secular Sunni in Iraq who kept power by eliminating a select few each year who might question his authority. As the Turks learned years earlier ' to keep Mesopotamia, all you needed to do is execute 100 people a year to deliver the message. The Iraqi Shia population is larger than the Sunni, so to keep them under control, the occasional surgery was required.
Saddam was good at it.
The same goes for Syria which is more Sunni than Shia. Assad is a member of the Alawi which is a Shia sect. To hold power in such countries one has to be prepared to chop a few heads. This is not a moral position, it is a statement of fact.
The US installing a Shia government in Iraq meant that now the Shias would naturally favor their own group to the exclusion of the Sunni. As Malakie would have had trouble resorting to the Saddam (and Turkish) tactic of selective assignations given the US 'moral' over-lordship he could not prevent the increase in Sunni dissatisfaction from gaining ground and now that inability has made a Sunni insurgency inevitable in the Sunni dominated North. Needless to say the Kurds also took advantage of this in their area.
President Obama wisely stayed out of Syria perhaps knowing that this was in essence a Sunni-Shia thing and certainly NOT the 'Syrian People' wanting freedom. If the Sunni's defeated Assad the first to have their heads chopped off would be the Christians, then scores settled down the list. That's what you do in those countries if your group takes over from another. In Syria it would be a case of out of the frying pan into the fire. As dictators go, Assad was not as ruthless as Saddam and in fact never wanted to be the leader of Syria. His lack of ruthlessness enabled the rise of leaders who have managed to give him a real challenge to his regime.
Saddam would have spotted them early on and made them disappear.
As the US wonders what to do it is time to really understand the simple dynamic of that region. Money talks and all politics are local. Religion is only a veneer to give one group the semblance of 'authority' over another. The Saudi's have been pumping money and arms into the Sunni rebels in Syria. It is as simple as Sunni supporting Sunni and the Saudi's are both loaded with cash AND arrogant enough to use that case to push their agenda. Immediately cut that off and tell the Saudi's in no uncertain terms to back off entirely or else. It's about time we realize the true bad nature of the Saudi's and their Wahabi nut-job clerics. Tell the Turks to cut off any aid they are giving also. The object is to starve the Sunni rebel forces of funds and ammunition which is flowing into Iraq. Stop the money stop the war.
Though Turkey and Iran (Syria as well) will have an issue with this; it is about time we let the Kurds have their own country and be done with it. That will stabilize part of Iraq. Yugoslavia divided into 5 countries; Sudan has divided, both on sectarian grounds. Why not Iraq which is a manufactured country created by Westerners? It should be three countries.
Meanwhile the current Shia regime in Baghdad needs to immediately do what the US did and buy off the Sunni leaders with lots of cash, give them some important positions in the government and promise autonomy of sorts OR accept the division of north and south along sectarian grounds. Unless you are going to bust heads as Saddam did you can't hold Iraq together unless you let everyone participate so no important group feels they are the underdog AND you bribe them with cash. That's how it works, pretending otherwise just gets people killed. We like to say it was the 'surge' that helped stem the violence in Iraq but it never was. What did it was paying off the Sunni leaders and buying their support.
We broke it so we have to fix it
So for the US, if it is our business in the first place ' we broke it so we have to fix it ' we should use the power of cash, NOT our troops. We don't even have to use drones or air strikes. Just hit up those consummate troublemakers, the Saudi's, and divert the cash they are fueling the insurgents in Syria and use it to buy off the Sunni leaders in Iraq. The rebel group is relatively small and once they have no money they will die a natural and quick death. Meanwhile, though it is politically incorrect to say so, we should secretly help Assad defeat the insurgents and stop Syria becoming part of the support system for the Sunni rebels in Iraq.