Back in the Jan-Feb 2003 issue of HSM, I presented Machining a Spiral Cam. I didn't have a rotary table at the time, but the cam was small so I mounted it directly on the shaft of a stepper motor to use for indexing. I chose to grind, taking very light cuts, rather than mill the profile and everything worked out. Photos later, on request, if anyone is interested.
To the question at hand: working inside is usually harder than working outside, but the principle remains the same. I would mount the workpiece on the rotary table, and after hogging out the material down to the minimum diameter of the spiral, begin taking successive cuts of suitable depth, each starting at successive degrees around the profile. This might leave a "rippled" surface that would have to be cleaned up with an additional operation - a drum sander or such.
A spiral of constant rate will have the successive cuts and successive starting points all equal and uniform throughout the process. A volute will be something else, as Paul suggests.
Weston Bye - Practitioner of the Electromechanical Arts - Author of The Mechatronist Column, Digital Machinist magazine