The Sunni Arab resistance is also not large, but it is fed by large amounts of cash Baath stolen from Iraq over the decades, and the realization that, once the Americans leave, the outnumbered Sunnis will have to face the wrath of their victims. The Sunni Arabs attacking American bases with mortars and rockets, and coalition troops with roadside bombs and ambushes, are taking lots of casualties (several times as many as they inflict). The U.S. decided, early on, not to comment on enemy casualties (the "body count game.") But reports from the troops indicates that the Iraqi attackers are taking a lot more casualties than the coalition forces. Most of these little battles involve no coalition casualties at all, but several Iraqi dead wounded and captured. But the response to Sunni Arab attacks has not just been to use UAVs, helicopters and superior training to kill lots of Arabs. The various Sunni gangs conducting the attacks have been identified and run to ground. Most of Saddam's key aides have been arrested or, in some cases, convinced to surrender. The U.S. has cleverly used the real fears (of post-occupation retribution) of Sunnis to get a lot of them cooperate.
American troops are doing a lot of the same clever improvisations in civil affairs that the demonstrated in the Balkans in 1990, and in Kuwait in 1991. Most Americans fail to realize how high the quality is of U.S. troops these days. The American military, especially the army, has kept raising personnel standards for over two decades. Troops are encouraged to use initiative and imagination to solve military, or non-military, problems they encounter. The reforms have gone on for so long that the entire chain of command, from top generals to new recruits are of the same high capabilities. Out of this has come hundreds of little innovations in dealing with occupied, or hostile, Iraqis. For example, every American army unit has undertaken some rebuilding efforts for the local Iraqis, and collecting information on those people to find out who's naughty and who's nice. There was some culture shock, but not as much as you think, for American troops have been training in Kuwait, and dealing with Kuwaitis for over a decade. So when the Iraqi preference for outrageous rumors (that American troops wore air conditioned flak jackets and sunglasses that gave them X-ray vision, Etc.) got in the way of collecting information, many troops just agreed with the Iraqis and implied that there were even more fantastic devices being used, so resistance was useless. To those Iraqis who admit to the Americans that the crazy stories were just typical Iraqi mind games, the U.S. troops let it be known that they will play the game to get the information needed to keep themselves alive.
The more perceptive Iraqis recognize, and respect, what the coalition troops (especially the Americans and Brits) are doing, and realize that Iraq's chance of success is more likely by cooperating with the coalition than in resisting or ignoring the "invaders." Iraqis who have spent time in the U.S. have gradually convinced most other Iraqis that the Americans just wanted to get rid of the dictatorship and go home. This is why most of Iraq is quiet, and the Sunni Arab areas are infested by Baath Party gangs that are spending most of their time trying to terrorize the mass of Sunni Arabs to either not work with the Americans, or join the resistance. But the Sunni Arabs are not a monolith. There are dozens of major tribes with strong tribal organizations. The tribal chiefs have been courted by American officers and diplomats, and convinced that Saddam is the past and something else is the future. Exactly what the future is, no one is sure.
The Battle for Baghdad continues, with groups of al Qaeda followers operating inside the city, and Sunni Arab groups operating in the suburbs and some northern towns. It's uncertain exactly what kind of plan the al Qaeda fighters have, other than killing lots of people with suicide bombers. Most of the dead have been Iraqis, which makes the al Qaeda "foreigners" very unpopular among Iraqis. But Baghdad is a big city full of many foreigners. It's easy to stay hidden in plain sight. Despite many tips, not many additional foreign Islamic fanatics have been picked up. But the small number of suicide attacks, and interrogations of the Islamic radicals already arrested, indicates that the number of al Qaeda/Islamic radicals is small and having increasing difficulty operating among an often hostile population. Even Saddam Hussein warned his followers to be wary of the Islamic radical "foreigners."