The problem is in the materials, the jets are brass which is soft but fairly dense material, the carburetor body is cast from powdered white metal that is similarly soft but far more granular in nature. Your challenge is going to be to drill only brass and not touch the white metal with your drill. The shape of the holes makes it impossible to drill all the way through, so that is going to require some precision drilling.
Best luck with the repair, if you can find a motorcycle scrap yard they will likely have plenty of replacements to choose from.