just this side of; one step short of; on the brink
Used to describe a state just before reaching a certain condition or location, often with a nuance of being very close but not quite there.
His attitude is just this side of rude.
The car broke down just before the station.
寸前 is more formal and often used for temporal immediacy (e.g., 出発寸前), while 一歩手前 can be used for both physical and abstract proximity.
Compound of 一歩 (one step) and 手前 (before, in front), literally meaning 'one step before'.