The most crucial battle going on Iraq is at the training camps for the new police, security forces and military personnel. This is little reported on, but Americans in the middle of the violence know that this training effort will decide the fate of Iraq. And it's no ordinary training. Like police and security force training in the west, attention is paid to the reliability and honesty of recruits. This is even more important in Iraq, because corruption is so much more extensive and debilitating there. For the new police force to be effective, they must be largely free of cops who can easily be bought. The selection process is more difficult than the training, and both must be done quickly, as Iraq won't be able to rule itself until it has a reliable security force. There have been a lot of success stories, but its the failures that cause the problems and some of these have been reported. A large percentage of the police and security forces recruited in Sunni Arab areas have been bribed by the Baath, or simply won over to the Baath cause (by promises of goodies once Baath is back in power.) While most Sunni Arabs know they have to go along with a democratic government if they expect any economic or political future in Iraq, they also have to deal with the murderous Baath Party members operating in their neighborhoods right now.
The tribal structure of Iraq, with more than half the population strongly identifying with a tribe or clan organization, provides one way to deal with Baath. The tribes are particularly strong in many Sunni Arab areas, and many tribes contain Shia and Sunni branches. But the tribal leaders have to be pragmatic. If Baath is too powerful in their area, the tribes will stand aside, or even cooperate with Baath. American Special Forces have been working with the tribes since 2002, and know how to make deals with then. This often includes providing protection from Baath hit squads. A lot of work with the tribes was turned over to American Civil Affairs units (who, like the Special Forces, SEALs, Rangers and Delta Force, belong to SOCOM) in the Spring of 2003. Now the coalition has a sizeable bureaucracy that just deals with "tribal matters." Some soldiers jokingly refer to all this as "The Ministry of Tribal Affairs." But it's a serious matter, as the tribal councils are the only organized and viable opposition to Baath in the Sunni Arab community.
There are hundreds of new political parties, most opposed to Baath. But that's the problem, there are too many political parties opposed to the one (now outlawed) Baath Party. While there are now factions in Baath, it is still fairly united, and even capable of cooperating with al Qaeda (which, for over a decade, has had the destruction of Baath as a top priority.) As a practical matter, Baath can't win. They can continue killing and terrorizing Iraqis, but their inability to do much damage in solidly Kurdish or Shia areas makes it impossible for them to regain control of the country. This is especially the case as long as coalition troops are still in the country. While the coalition troops want to go home, and probably will do so a lot sooner than most people think, the ticket home is paid for by creating an effective Iraqi police force. Most coalition troops in Iraq know this, for it's not just the trainers and advisers who work with the new Iraqi police and security force. The coalition combat forces work with the Iraqi police every day, as do the coalition troops who move along Iraqi roads daily. The "war" ends when the Iraqi police can keep the peace everywhere in Iraq.
Most Iraqis know what's going on, that they care caught in the middle of another civil war. It's not a particularly violent civil war. One or two car bombings a day, and maybe half a dozen assassination in a population of twenty million is not exactly widespread violence. But it's pretty obvious that the people who backed Saddam Hussein for decades, the Sunni Arabs and their Baath Party, want to be back in power and are willing to do what they do best to get there. Baath was always excellent at media manipulation (inside and outside the country) and the use of terror. Talk to Americans in Kurdish or Shia parts of the country and they'll say, "what war?" But in Baghdad and it's suburbs, plus some northern cities, there are lots of Sunni Arabs, and support for Baath.
Coalition commanders are pretty sure that Fallujah is being used as a base for many of the more recent attacks. Captured terrorists always seem to know someone "from Fallujah." The "Fallujah brigade," using Sunni Arab ex-soldiers to police the city, has failed. But in a dry run for the turnover of major decision making to the interim government, the coalition is trying to get the interim leadership to make a decision on Fallujah. The Iraqis know that, while they don't like a foreign army occupying the country, without the foreign troops, Baath and it's army of torturers and terrorists will retake control of the country, or kill lots of Iraqis trying. The secret shame of Iraqis is that they were not able to get rid of Baath on their own. Oh, they like to blame others for that (the UN, the US, International Zionism, whatever), but many Iraqis will even it admit that, well, it is an Iraqi problem.