I have a horizontal lock, "average" size although to me it seems a little narrow. Anyways the very tip of the key broke off in the lock. I tried to get it out and managed to not only push it to the back of the lock but get it wedged in there. I really don't want to call a locksmith and quite frankly don't have the extra cash to do so. The lock is too narrow for tweezers. For all that is holy and all that is not someone please help me!
Do you have a set of lock picks? There is tool in there called the key extractor, that can use to push past the pins (by pushing them up with the top), and the reach beyond the broken key piece, hook into it and pull it out.
Just out of curiosity, did it snap off on a deep cut in the key?
If it is unlocked, Just take it apart. If it's still locked you'll need an extractor. Buy one and wait days for it to show up or call a locksmith and pay maybe $50.
For reference, this is what the extractor will look like. It would cost a couple bucks, plus shipping (though for the cost of shipping you may want to invest in a basic pick kit that comes with the extractor).