There never was that large of a "central support base." This myth was harped on by anti-war types, some of whom even assigned such support to "a majority" of Iraqis.

In fact, there were just the Baathist fighters, their erstwhile terrorist Islamist allies, and maybe a couple hundred thousand supporters who don't want to fight, but actively help with supplies and concealment.

The rest of the Sunnis (about 5 million, I believe) certainly enjoyed favored status under the Baathist regime, but for the most part did not themselves participate in atrocities.

I believe they are mostly terrified of the insurgency while at the same time terrified of a feared revenge by the Shiite/Kurd majority. As it becomes clearer that the latter is not going to be the case, more Sunnis will come around.