Margaret,
I've used a few approaches in the past on similar problems. First, there's the easy-out tool. Looks like a small punch with ridges or left hand threads along its working length. First, you carefully drill a certain size hole in the EXACT center of the screw body, then you gently hammer the easy-out tip into the hole. Lastly you slowly turn the easy out counter clockwise and if you're lucky, it brings the screw out with it.
The second approach is to find or fashion a tool called a gouge out of a punch or chisel. Shipyard machinists use them all the time. The gouge will look sort of like a narrow chisel with a assymetric V-shaped tip. Gently tap the tip of the gouge into the outer perimeter of the screw in a counter clockwise direction. If you're lucky, it will "gouge" itself into the screw's metal and start turning it out. Continue patiently and gently tapping the gouge until you have enough metal to grab with a pliers or visegrips and bring the screw the rest of the way out.
If you haven't guessed it yet, these are both delicate operations, kind of like a mechanic's equivalent of brain surgery, so I can't recommend either for a beginner or the nervous, especially on something as delicate as a pot-metal carburetor. Which brings me the third approach: pull off the carburetor and bring the whole problem to a good machinist!
If all else fails, I have a spare Thermoquad (destined for ebay) with a somewhat worn throttIe shaft I'll sell you cheap plus shipping. Hope you can fix yours, though.
Carburetor problems can be maddening. It took my expert mechanic in Taegu ten attempts at my used Edelbrock carb to get it to run evenly on both sides. You get one right and you want to leave it the h**l alone forever!
Good luck,
Steve in Korea