[sofere]

You're in the BB next hand, assuming he pushes and shorty folds, you have to fold and next time you get a chance to push you'll have absolutely 0 fold equity. So I think this is much less risky than waiting to push into BS.

My thought is...it basically guarantees that shorty will either (a) have to showdown this hand, or (b) will have 100 chips left and be all-in in the SB next hand.

4 things can happen:
(1)BS overpushes, BB calls, you fold
(2)BS folds, BB pushes his last 100, you call
(3)BS overpushes, BB folds, you fold

If he's all-in this hand vs either you're any 2 or BS's any 2, he's 50-50 to bust. Whether BS pushes, BB calls and you fold, or BS fold, BB calls, BB is ~50% to bust and if he wins is about even with you. Assuming you are then 50-50 to bust before him then there is a 75% chance you make the money. (1- (50% chance he wins * 50% chance u bust before him).

If BS overpushes and BB folds, you fold i think you're in a very good spot.

One last thing that can happen is BS calls, BB pushes his last 100, you both call. Most likely this is getting checked down and is an ideal situation. If BS pushes the flop just get out of the way.