Depending on the action in the shot you may need to separate the actors head from the background. If I knew I wanted this kind of effect I would have shot a clean plate with the actor not lying on the pillow so I would have had something to fill in the hole behind the actor when the head was spinning.
If the actor is already thrashing around you might want to animate a soft edge mask around the actors head and then start experimenting with the effects that Roei suggested. You might even want to try some directional blur, radial blur, displacement mapping, or other distortion effects. The mask will allow you to limit the effect to just the actor's face using the compositing options available in AE. Maybe something like this:

I think the key to pulling this off is going to be some roto work. You at least have a couple of ideas to play with. If we could actually see the shot we might be able to give you some better suggestions.