If you drop to a lower stack (e.g. you only have 15-20 big blinds left) your range of playable hands gets smaller and smaller. You should switch to a "push or fold style" with that kind of a small stack.
push/fold at 15-20 big blinds is overkill IMO.
even when i'm legit short-stacked (like 8-10 big blinds), i like to mix in
stop-and-gos rather than just open shoves.