I second the vise-grips recommendation. That's what I used to do on my old Oscar Schmidt after the chrome tuning pin became stripped. (I ultimately solved the problem by switching to Keith Young custom 'harps.)
I also agree that if your autoharp is truly new, and a pin broke, you should try taking it back. If they won't replace the autoharp, they should at least cover the cost of repair. I suspect they'll be more likely to replace the instrument.