put your text on a straight path and convert to outlines - use the free distort tool to taper the text or use a tapered rectangle (what are they called? Truncated triangle?) as a shape to define a warp. Drop your tapered text into the brushes palette and make it an art brush - draw the required spiral shape and stroke it with your brush. You can scale the brush to fit your spiral in the art brush dialogue. You may also have to reverse the direction of the brush to get the thick end outer-most.
