The Iraqi groups represented included Kurds, Summis (sic) and Shiites, and others who have spent years in exile. All were specially invited by the US.
The Shiite faction that boycotted and demonstrated is the Iranian-backed Iraq Islamic Revolutionary Council (IIRC). The more moderate Ayatollah Ali Mohammed Sistani faction attended the meeting. (Sistani issued the Fatwa telling his followers not to impede the U.S. forces in the first week of the war). The potential secular leader of the Sistani faction, Khoi, was assassinated last week by followers of the IIRC.
Hopefully the rest of the Iraqis that participated have sounder minds and that a bona fide alliance among them can be achieved.
Among the "rest of the Iraqis" were the Sunnis. Saddam's Baathist party and Osama Bin Laden are Sunnis, as are most of the corrupt Arab leaders. The Shiites are the Iraqis that were slaughtered after the first Gulf War, and some believe that the historical DOS preference for Sunni dictators (e.g. Saudi Arabia) had a lot to do with our looking the other way.
The situation in Iraq, and the factions involved, couldn't be more complicated; it will take some mighty fancy footwork (and a big stick) to make them cooperate, not to mention some arm wrestling between the DOS and the DOD.