5twins, I'm pretty sure he has it right, it's the mix screw.
What happens is someone screws the mix screw in until the brass tip shears off and gets stuck in the carb body. So, you drill a hole in the body on the opposite side until you reach the air mix cavity, and push the nub back out.
I had a carb set with this problem, and this solution never occurred to me. So I sent it to an expert who will remain unnamed. He did the drill-out and really screwed it up. I was able to fix one body with much time and work, but the other was destroyed.
So, rwilkens, you probably have carbs that are beyond repair. If you want to send them to me, I'll see what I can do. Your other choice would be to try to buy two bodies off of this forum. Maybe from me. Or, buy a parts carb on eBay. I just got a nice ebay deal on a set of parts carbs that were all there except for the slides. People cannibalize the slides out of carb sets because slides with good diaphragms are valuable.