ISIL's project is a year matured in Syria, where public opinion has long since turned against the extremists
The first step to dealing with these fighters would be to change the composition of the government from pro-sectarian al-Malaki to another candidate who's actually willing and able to produce a unity government.
It's because of the tacit support of Sunni civilians and overt support by Sunni militias that ISIS/ISIL has managed to gain such a powerful foothold in Iraq. Civilians give intelligence and places to rest and hide; Iraqi Army soldiers get the cold shoulder. It's the same reason how the British failed so miserably to keep ahold of their empire, especially with regard to their nearest province: Ireland.
I get that the US doesn't want to intervene anymore than we have to in Iraq. However, calling for al-Malaki to step down and to have a new unity government would be a good political maneuver to heal this division that Republicans in America and George W. Bush exacerbated in Iraq. I would also offer the Iraqis the option of having us fly combat missions over Iraq to keep up pressure on ISIS/ISIL. The insurgency will not leave until the political questions of Iraq's governance have been answered conclusively and in the favor of all Iraqis. Even then, there will be a few people who will continue to fight, even if military operations and public opinion have turned against them. The difference is that these individuals should only be isolated individuals that could be arrested beforehand, with intelligence from the civilian population, such that they cause no harm to anyone. Humane treatment, as defined by Iraqi culture and sentiments, is the best way forward for dealing with the lunatic fringe (bearing in mind, that it may not be the same as American sentiments on the issue).
Think about it.