Turkey is much more of a concern.
The one portion of Iraq that is functional is the northern Kurdish region. As the balance of the Iraqi state continues to deterioate, it is inevitable that America will eventually remand more control of this area to the Kurds while it tries to pacify other regions. In turn, the Kurdish population will become more brash in their demand for a de jure state separate from Iraq, as it has existed de facto since the Gulf War.
The trouble is, Turkey has a very sizable Kurdish minority bordering upon northern Iraq who would undoubtedly display a great deal of sympathy for their Kurdistani bretren. But, as the only multicultural, secular Muslim state in the region, Turkey is very keen to resist nationalist sectarianism within or along its borders.
Assuming Iraqi Kurdistan becomes independant, either in thought or in fact, Turkish Kurds may come to place crushinginly fatal demands on the only secular Muslim state in the region, thereby opening a wound for the fundamentalists to salve.