The reason these jets will not come out is due to the incorrect size and shape of the driver used to install them the last time they were out. Do some searching in previous "Carb rebuild" topics and you'll see several pictures of the 3 drivers made specifically for the idle-jet, idle-jet cap and main-jet. The critical one being for the idle-jet itself. The slightest burr or deformation will cause this issue.
You have stated the jet is loose. The carb must be stripped of parts. If you have an idle jet as a sample, grind an appropriate sized driver to fit (see previously mentioned photos). The fit is very important for both removing and installing. There are more details in that write-up.
Apply penetrating oil to the jet threads and using "the modified" driver, screw the jet in and out repeatedly until your hand cramps ! The more times the better ! DO NOT TIGHTEN. When you feel the jet start to make contact at the bottom - STOP. This may take several attempts. By repeatedly threading in and out the burr/deformation will be reduced. Over a large card-board box and holding the carb so the idle jet will fall into it, apply full air pressure to the idle-screw port. The idle-jet should blow out.
If not: With the jet loose, heat the carb body and apply air pressure, again. Keep in mind there are seals on the throttle shaft. Common-sense here for the heating! 200f is enough ! See the same article for how I heated carbs using a card-board box and a small electric heater. ( common-sense with this too !)
if not, keep repeating.
Drilling is the last resort. Drilling will ruin the jet and very probably ruin the internal threads.
Burrs can be removed from the jet with a jewelers file. If you don't have one - buy one ! When cleaned of burrs and when Re & Re'd with the correct fitting driver, they jets will fall out, next time.