This is the point of desperation. People either play until they are blinded to death, or they start pushing when they have ANYTHING appealing. Do not just get blinded to death. Pushing your whole stack with a non-premium hand sucks, because if you run into someone with a good hand, then you're likely out of the tournament. But always remember that aggression pays off at NL holdem. You're in a better situation if you push around that remaining stack, as opposed to just sitting on it.
You have to decide what you want to accomplish. Since your tournament stack is dwindling, then you need to start picking up the blinds to build your roll. When you push all in, you want people to fold. Especially in these situations. You are only looking to pick up the blinds here, because you are raising with a sub-premuim hand.
If it gets to the point where I have 5-6xBB, then I will start pushing with anything reasonable. Any 2 paint cards, any pair, etc.
Back to your original question, I don't have a forumla. It depends on my stack size, and my opponents stack sizes. Say I'm in a NL tournament, and the average stack is 3500. Blinds are 100/200 with a 25 ante, and I'm sitting on 1100 chips. I have to start making a decision soon, because as people get eliminated, the big stacks only get bigger. When you get down to 700 or 800 (and you go all in), these big stacks will call you with suited Kings, Ace-blank, and QJos. See what I mean? They aren't scared of 700 chips, especially when they smell an all-in blind steal because your back's against the wall. You want your raise to make the other person think: "Shit. I have him covered, but if I call here AND LOSE, then I just lost a chunk."
Note: This could all be wrong - but that's just how I see it.
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