The delays are being caused by Maximum Aircraft on Ground (MOG). There is only so much ramp space and spare taxiways to park and put aircraft. Additionally, there may be limited numbers of air stairs, electric carts, air carts, loaders, and fuel (to name just a few). You can only put as many aircraft through an airfield up to what your ground support can handle.

This is where the USAF will shine. A C-17 can pretty much operate autonomously without the need for much ground support if any. Additionally, they can perform a star-point turn and be able to turn around in as much space as 90 feet (dimensions may be wrong but I know I'm close). To put that in perspective, a C-17 has almost identical dimensions as a DC-10.

As of yesterday, the news media was already complaining "why is it taking so long". This is the same garbage we heard after Hurricane Katrina. And the military response to Haiti has been almost identical to that after Hurricane Katrina. The problem with Katrina was the local state government (LA) did not ask for military help and therefore, it is illegal for the military to go in until this crucial and necessary step is performed. The Federal Government labeled the Gulf Coast a disaster area before she hit, but it didn't mean anything until they official asked for help. And there was a significant delay in that request.

Additionally, you have a lot of countries sending aid and it is probably uncoordinated. Until the military gets 100% control of the airfield and command and control set up, you're going to have airplanes hold and get refused.

The silver lining in this disaster will be that the military and first responders will learn a lot in how to better deal with disasters like this for the future.