I don't think the U.S. or Iraq will feel too good about Turkish troops crossing into Iraqi Kurdistan.
I also think the Turks lost their "high card" in the dispute once they told the U.S. to 'kiss off' during Operation Iraqi Freedom when we wanted to have Coalition forces come through Turkey for the Northern Front. Instead we had to air drop troops and equipment into Kurdistan. The U.S. forces fought along side the Kurdish Peshmerga in taking on Hussein's regime and that further cemented the bonds of friendship.
The U.S. Military is right now building military bases in Iraqi Kurdistan - what many believe will be where U.S. troops will eventually be based to ensure stability in Iraq and the region. I don't think the U.S. military will feel too good about incursions into that area by the Turkish Armed Forces.
I just love that ad. Every time I see it, it makes me smile...and given the news over the last week or so, that's saying a LOT!