I know that this won't be popular, but I would extend deployments rather than rotate troops home during actual combat operations. I remember seeing an interview with a high ranking Vietnamese officer, possibly even General Giap, where he explained that one of the biggest advantages that they had was how quickly the US forces were rotated out. By the time they learned what to look for, they were at the end of their tours. It would seriously suck for the ones deployed, but your casualties will be much lower if your line troops are veterans.
That being said, we are well beyond what I believe should be considered "combat operations" -- there is no opposition army to fight. Once the Iraqi military was defeated, the US should have redeployed to secure the country's borders and make the Iraqis police their cities. Our armed forces should never be used as police or for "Nation building". That line about, "We expected to be greeted as liberators" indicates that US leadership had no clue about attitudes toward Americans in that part of the world. I don't know if they're lying when they say things like that, or if they're just dumber than rocks.