I rebuilt some carbs that had been exposed to water & one screw broke off. I was able to drill it out in my drill press. My local hardware store had the drill & tap set, as well as all the screws. I think it was a 2mm, or 3mm. I can check for you. I think the one that broke on me was the needle pin retainer screw though.
Some of those screws can be crazy tight. What I have done when they don't come out easy, it set the carb body in a hydraulic press, with the press pushing down on the screwdriver. I don't give it much force, but its just enough so that when I turn the screwdriver with a wrench, there's way less chance of the screwdriver backing up & stripping the heads of the screw. (hope that makes sense)