As I recall, GEN Shinseki was canned because he publicly disagreed with Rumsfeld on the number of troops to use to take, hold, and pacify Iraq.
Looks like Shinseki was right, too. Oops.
I would have probably agreed with you up until 6-8 months ago. The tipping point in part was due in part to the surge, but I would argue that the real change occurred when the Iraqi people decided for themselves that living under terrorist control was not a good thing and that supporting their government and the Americans was a better option.
Yes, we probably should have sent in more troops in the beginning but living daily under control of the various militia groups was what made Iraqis start selling out their captors to the the U.S. Once they saw that the U.S. could deal effectively with the militias, they joined us in defeating them.
We did so with far fewer than he suggested was needed. What we didn't do was to 1)attack from the north and grind up the northern nutballs, 2) significantly increase the size of the standing military to account for rotations, and 3) keep Iran out of it...which was largely a matter of poorly dealing with Democrats and the State Department.
Those that said we needed more troops in the initial invasion were shown quite clearly to be wrong...and we still aren't to their expected casualty levels.