^^^like that. guessing it's been done a few times.
That idle orifice is a tiny opening in a soft metal housing, currently jammed with a little piece of soft metal. If you can see and reach the tip of the needle when you pull off the plug, might first try a bladed screwdriver to gently push it back out. Failing that, the little dimpled top of a finishing nail might work to push it out, bending the nail to get to the right access, maybe some leverage with a bladed screwdriver. Maybe a little lube or carb cleaner on the possibility that some corrosion is going to fight you -- might help. can't hurt.
If that fails, try F_R's solution -- could use a finishing nail as the prod, drilling a hole to fit the nail (maybe 1/8"?). Can see how that trick could work well, but think I wouldn't grab the drill unless it's a last resort, like F_R says.
All this talk over a tiny little bit of busted metal. Best thing is, probably won't break off another one very quickly -- also get to see how and where they seat.