Those get stuck rather frequently. Im not sure exactly how the Carters are setup, but with my Zenith, I soaked it in a little vinegar overnight and then used an air compressor to blow air from a passage on the bottom of the float bowl which cause the pressure to push it out right out.
On mine I broke the small circlip that attached the brass head to the shaft, and I ended up cleaning it up and was able to solder it.
In case I misunderstood, have you been able to remove the top half of the carb?
Jeff