All you need to do is edit the texture for that object. That texture will hold your 2d image.
As Silkrooster said, apply whatever you want to rotate as a texture to your 3D shape.
would you mind explaining how to edit the texture while still having control of what the picture looks like?
Also, the 3d curved object was made in another program and it opens in photoshop. It is not one of the shapes listed under "new shape from layer" in CS4.