The US will gladly leave it to the Iraqi Government, when they are capable.

al Jazeera:

Iraqi group 'splits' from al-Qaeda                  
Al-Shammari: Al-Qaeda has a different agenda from that of the Islamic Army in Iraq [Al Jazeera]

One of Iraq's main armed groups has confirmed a split with al-Qaeda, according to a spokesman for the dissenting organisation.

Ibrahim al-Shammari told Al Jazeera on Thursday that the Islamic Army in Iraq had decided to disunite from al-Qaeda in Iraq after its members were threatened.
        
"In the beginning, we were dealing with Tawhid and Jihad organisation, which turned into al-Qaeda in Iraq," he said, his identity obscured for security reasons.

"Specifically after Abu Musab al-Zarqawi died, the gap between us [and al-Qaeda] widened, because [they] started to target our members."

Al-Shammari said al-Qaeda in Iraq was in pursuit of a different agenda to that of the Islamic Army in Iraq

"They killed about 30 of our people, and we definitely don't recognise their establishment of an Islamic state - we consider it invalid.

http://english.aljazeera.net/NR/exeres/37A1B44F-F804-40C5-BF5E-9699FD1B67E3.htm