The US military, in short, sucks at insurgency, occupation and colonial style warfare. It is brilliant at battlefield operations outside of major urban centers and is probably, as a whole, the premier battlefield supremacy army in the world today. The Gulf War showed that very clearly. And, indeed, if the US military had blown into Baghdad, toppled the regime and left in 6 months, everyone would still be trembling in fear.
What the US has, then, is a decapitation military. It’s very good at knocking off governments, but not so good at guaranteeing what happens afterwards.
The biggest political mistake the administration made in Iraq was trying to run it. Americans do not have the Patience for long wars that do not involve an existential threat. John Mueller points out that
American troops have been sent into harm's way many times since 1945, but in only three cases -- Korea, Vietnam, and Iraq -- have they been drawn into sustained ground combat and suffered more than 300 deaths in action. American public opinion became a key factor in all three wars, and in each one there has been a simple association: as casualties mount, support decreases. Broad enthusiasm at the outset invariably erodes.
If we had taken down the regime, did our WMD search, tossed the keys to Chalibi, and bailed the political and (more importantly) geopolitical consequences would have been much smaller. Iraq still would have gone to hell after the fact (and Chalibi probably wouldn't have lived real long) but it would be an embarrassment, not a catastrophe, and our military would still look omnipotent. Now Iran is cheerfully building nukes while inflicting the death of a thousand cuts on the US military. The Norks are playing nuclear rope-a-dope again. Our soaring debt has set us up for another round of economic pain, ala the stagflation 70s. Meanwhile the army will need several years of retooling to get "unbroken".