The frontiers of Kurdistan go into Iraq, Iran, Syria and Turkey. The latter country would go to war if any part of its soil was threatened, or someone tried to splinter it away. If the United States forces upon Turkey an autonomous Kurdistan region, Turkey would turn politically against the United States.
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Neither the United States nor Turkey want this to happen, so it will most probably not happen. (Already the American military is assisting Turkish troops and black bag operatives in South Eastern Turkey to hunt down and exterminate "extremists", i.e. Kursdish separatists such as ex-PKK men.)
On the other hand, the American interest coincides with the Iraqi Kurds' interests, who are currently the most loyal allies the U.S. ever had in the whole of Middle East, after the Israelis. The U.S.
wants the northern region's oil to remain under the control of the Kurds, more than anyone else there.
Other considerations:
The oil in southern Iraq is mostly in areas where Shias are living. (Same goes too, naturally, for Iran..) Besides everything else, why would anyone in the U.S. would want to encourage a scenario whereby the most precious commodity in the world falls into the hands of the more anti-American and extreme kind of Islam?
But I would be very curious to see how someone like Tony "The Poodle" Blair would react if the prospect for partitioning Iraq is floated by Washington! The British imperialist tactic of creating totally artificial borders in colonised countries or ex-colonies is the cause behind most of the troubles in the Middle East. Partitioning a country along strictly ethnic/religious lines, i.e. in a rather "logical" manner, has always been abhorred by Whitehall.