for things like that which are not rusted or galled in place by dissimilar metals i would use a solvent (such as fresh gas) or wd-40 and just screw it in and then back out in and back out. it seems a little suggestive but i have done this on lots of little things i didn't feel comfortable using pressure on and it eventually works. just wipe the threads with a q tip or my favorite, a gun cleaning cloth, super cheap and low lint, to get the residue you have freed up of the threads.
then relube and repeat, after a while it will come further and further out.
too much force can deform, widened shrink or close off the tiny idle jet hole . so take your time and then when you get it out.......... clean the shit out of the threads inside and out so it doesn't stick in the way back in!