To prepare one's self to put forth greater effort in overcoming an obstacle (of any type; physical, mental, etc.)
origin - (probably military drill sergeants) preparing for any strenuous physical task invariably requires fully engaging the stomach muscles and the more overweight the person the more it manifests visually as sucking up the stomach.
Suck it up and re-shoulder that pack.
Either Private Gump sucks it up or the platoon'll gimme twenty more pushups.
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