No matter his raw ambition, The Caliph will have to get his act together. A lot of Syrian jihadi outfits have turned against IS. The same thing is happening in Iraq; Sunni militias are turning against them in Nineveh province.
Enter tribal Sunni sheikhs - the ghosts in this infernal machine. The Caliph must have enough trusted moles to tell him that once the sheikhs have finished using IS as a tool to "destabilize" the al-Maliki administration in Baghdad, they will definitely advance to smash the caliphate. This is an extremely temporary alliance of interests - a sort of remix of the previous Islamic State in Iraq having its emirate smashed because of the American cash-propelled Anbar Awakening.
The Caliph will also have to face Athel al-Nujaifi, the governor of Nineveh province; he wants a different Sunnistan with a high degree of autonomy (and lots of still unexplored oil) but still inside Iraq. Al-Nujaifi is the most influential Sunni politician in Iraq and head of the largest Sunni political party. For the moment, The Caliph seems to be taking no chances. IS operatives have arrested scores of former Iraqi army officers and Ba'athists around Mosul.