The Pup makes some excellent points above. The terms short stack and big stack are irrelevant without the context of number of blinds left and tournament position.
In a large MTT, you can have a huge stack (100xBB) while some others at the table have 10BB or less. At that 10 or less mark, a decent player should be waiting to shove as soon as they get a winnable hand. I think usually holding an Ace, Faces, or a pocket pair would be enough to shove. Remember the range of cards you are likely to face before you call with some junk J7.
In a small SnG or right on the bubble, a small stack can potentially be a bit more patient waiting for a hand, but at some point they have to shove and most of the time have at least a good high card. If the stakes are low enough, they might shove with anything if they took a significant tough beat a hand or two earlier. The philosophy of getting back in the game by doubling up or entering a new one plays in here.
I know there are some who push with anything with a small stack. At 2 or 3 BB left, I can see that, but 5 - 10BBs gives you a couple of rounds. If it's bubble time, its better to fold that K10os and home someone else gets antsy. You will hate the decision to push when the villain (usually big stack) calls your push with A3o and wins the pot with Ace-high after the board misses both of you.