All-in in Baghdad?

The Wall Street Journal reports what some folks have been saying for the past week or so — that with Donald Rumsfeld gone, the military is calling for a new push to stabilize Baghdad. The consensus, according to the article, is that 20,000 to 30,000 additional troops would be needed. With that force, some argue, we could sharply curtail the violence. As retired Gen. Jack Keane puts it, “the notion that we can’t provide protection for people in one of the capital cities of this world [Baghdad] is just rubbish.”
This matter is beyond my expertise, but consider me skeptical. Baghdad is a sprawling metopolis of something like five million people. Considering how easy it is to blow things up and to kill dozens of people at a time, and given the existence of various extremely well-armed militias and deep antagonism between the Sunni and the Shia residents, protecting the people of Baghdad is surely a daunting task. Recall how, for an extended period, Israel was unable to prevent a steady stream of lethal suicide bombings by outsiders in cities where its police and army had a complete monopoly on force.
Moreover, suppose that, by adding 30,000 U.S. troops, we did stablilize the city. It’s highly unlikely that we could sustain this troop level for long given the strain on the Army and Marine corps. After a while we would draw our forces down, and the Iraqis would have to ensure stability in the face of the same antagonisms and re-formed militias that plague the city now. There are parts of Iraq where these forces are willing and able to do so, but I doubt that Baghdad is (or will soon be) one of them.
There’s not much point in launching a huge operation in Baghdad unless we’re prepared to sustain it at something like the same scale for at least several years. And sustaining it at that level may not be feasible, either operationally or politically.