patience and containment in Iraq and Syria

That's the recommendation from Stephen Biddle and Jabob Shapiro. They base their conclusions on the historical record of civil conflicts: they usually end only after the warring parties are exhausted and often when they lose external support. They also argue that there is no easy way to protect U.S. interests.

In the absence of a mutual willingness to end the war and accept some new model of representative governance, even great progress against ISIS does not realize U.S. interests in the conflict—which are to end the terrorism threat, the humanitarian crisis, and the danger to regional stability, not merely to occupy the city of Raqqa. A mutual willingness to end the war on the part of most or all of today’s warring factions, however, seems a long way off.
In this context, real U.S. leverage to bring about a real end to the war—and actual realization of American interests in that war—is distinctly limited. None of the proposals popular in today’s Washington debate offer any meaningful prospect of achieving this. According to U.S. military doctrine, to defeat even an insurgency (much less a proto-state like ISIS) and stabilize a threatened population requires something like 20 counterinsurgents for every thousand civilians. That means 50,000-100,000 well-trained troops would be needed to hold the area now under Islamic State control (depending on how much of the population has fled), much less the rest of Syria. No one is now proposing a realistic plan to accomplish anything close to this—whether such a force comprises American troops, Iraqis, Kurds, Saudis, Turks, or anyone else. In the absence of this, bombing raids or offensives from Iraqi or Kurdish allies can accelerate the rate at which ISIS burns through its capital and perhaps hasten the day when the Islamic State is replaced by the next militant group in the queue—but limited efforts of this kind cannot end the war.

Sober analysis from serious scholars.