The Turks ask too much

According to Bloomberg,

Turkey called on U.S. forces to seize Kurdish fighters in northern Iraq, as the Iraqi government warned against a Turkish invasion of the oil-rich region.

The U.S. should extradite the militants to Turkey to help prevent an attack on the rebels' bases in neighboring Iraq's Kurdish-controlled north, Egemen Bagis, an adviser to Prime Minister Recep Tayyip Erdogan, said today.

The US might be able to free up some special forces to seize a few of these guys, but the politics on the Iraqi side would get really complicated. What happens in the Iraqi government if the Kurds decide to "punish" the US? (Extradition is, I'm sure, off the table.)