I have an inexpensive Homelite gas weed trimmer that fell over and the plastic choke lever broke off. It's only about 4 years old and the motor works fine. It probably hasn't even been run for more than an hour in the time I've had it. Even though a new one is probably only $79.95 I don't want to just throw it out.
Anyway, this cheap part is all plastic and has a shaft about the diameter of the q-tip shaft. It snapped off flush with the housing that it sits in. It doesn't look as though trying to super glue it would work.
What I'm thinking is trying to find some way to jerry rig it. You have to be able to set it on 1, pull the starter cord a couple of times, then set it on 2 and start it. Once it warms up, then you turn it to 3. Some sort of a screw would probably work, but where could I find a screw that's really small, but with a big head?
Otherwise, if I could put some sort of a re-inforcment inside the shaft- a very thin rod of some sort, that might work, too. The thing is really small, though, so drilling holes that size would be tricky.