I had a key break some years back in another car, with a portion still in the ignition switch. Had to call a mobile locksmith to the car and my wife at home to bring spare key. Locksmith picked out stub with no problem in about 10 minutes, minimum 1 hr trouble call. Root cause was crack in key.
BTW you should have PATS but the code is in the plastic part of key, you should be able to see a small rectangular insert 1/8 x 1/4" at end of key.
p.s. Problem with short piece is tumblers drop behind preventing a straight extraction. Each tumbler has to be picked, stub moved outward, pick again, etc.