The US isn't supporting extremists in Iraq, and the people their fighting right now are the ba'ath loyalists.
The people leading the fight might indeed be ba'athist elements from Saddam's old regime. However, there's also plenty of people left impoverished and in destitution because of the failure of the Bremer/Bush regime to properly manage post-war Iraq, where the free market absolutism failed the common people of Iraq spectacularly. There are also people incensed by the US puppet interim government and repeated acts of desecration of holy sites, ranging from the casual mosque to the holy city of Najaf.
You can't pin this insurgency on just ba'athists. It's an uprising that would not have occured with the ferocity and pervasiveness if we had managed to quickly implement security and had a realistic plan for reconstruction in place. It would have still been there, but it would not have taken over large swaths of the country like it has now.
Regarding the footage, it appears that Fallujah will not be a habitable place for a long time to come. Even if people do move back in, the cleanup operation and the restoration of basic sanitation and utlities will take a very long time-and is unlikely to get very far with an insurgency that is only controlled as long as the US armed forces are present in large force.
It appears that while we've been working on Fallujah with such ferocity, other exisitng problem spots such as Mosul gets worse. Are we going to deal with those problem spots in the same way? How much of this country do we have to devastate in order to liberate it?
Iraq is just FUBAR, in the most literal of senses. There's no way to hold a reasonable election that would form a coalition government that would reprsent Sunnis, Shiites, and Kurds alike and do so in a manner that would represent all of the groups equitably without introdcuting a kind of federalism that would make the country's neighbors very uneasy. There's a good risk of the tyranny of the majority in the elected legislative house. There's the huge influence of a few powerful clerics with large amounts of public power. Finally, there's a massive security problem that is probably beyond recovery at this point.
No way out folks. People might berate me for my nihilism on this one, but there's no way to win this one without turning our gameplan completely around.