What you need to do is compress the spring that pushes the plunger/needle (for lack of a better word) back down and then you will be able to remove the cable from the plunger/needle.
Clean the plunger/needle assembly, lube the cable up real good or replace if necessary, and clean the part of the carb where the choke goes in and you should be good as new.
Cheers.
EDIT: sorry I just realized what you were asking, you can't get the needle out of the carb at all?? There shouldn't be anything holding it in, spray some carb cleaner in there di disolve the gunk and yank it out.
Good luck