Okay, lets suppose that the US military isn't already busy fighting other battles, let me ask you this: Do you seriously think people would be in favor of having their tax dollars spent on the invasion of a country that doesn't Harbor the Islamic terrorists that attacked their soil, doesn't have any resources that can be exploited, and has done little to no trading with the U.S. ?
You're basically acting like Woodrow Wilson before the first world war, and also you have to keep in mind(I mentioned this earlier) that literally hundreds of soldiers have been in the region trying to defeat the warlords. If the US shows up what will they do differently than the combined might of the UN and the African Union? use drones? use nuclear missiles? You say Iraq muddies the debate, Okay, so what about Afghanistan? is that region significantly more stable than it was almost 10 years ago? What about what happened in Vietnam? is that now a democratic country? How about the attempts to stop the spread of socialism in Latin America?
The people don't need more carnage. If you go in you'll destroy whatever shards of infrastructure they have left, and the situation will truly be hopeless. If you're in favour of sending a small amount of soldiers to supplement the peacekeepers already present in the region to tackle the government while simultaneously building roads, hospitals, schools and strengthening Agriculture then I totally agree with you, but to suggest that they need to be invaded for their own good is simply treating an infection with a butcher knife instead of a scalpel.