Depend on a small thing or be at risk.

synonym: hang by a hair.

Roget 665: be in danger etc. adj.; be exposed to danger, run into danger, incur danger, encounter danger etc. n.; run a risk; lay oneself open to etc. (liability) 177; lean on a broken reed, trust to a broken reed; feel the ground sliding from under one, have to run for it; have the chances against one, have the odds against one, face long odds; be in deep trouble, be between a rock and a hard place.    hang by a thread, totter; sleep on a volcano, stand on a volcano; sit on a barrel of gunpowder, live in a glass house.    bring in danger, place in danger, put in danger, place in jeopardy, put in jeopardy etc. n.; endanger, expose to danger, imperil; jeopard^†, jeopardize; compromise; sail too near the wind etc. (rash) 863.    adventure, risk, hazard, venture, stake, set at hazard; run the gauntlet etc. (dare) 861; engage in a forlorn hope.    threaten danger etc. 909; run one hard; lay a trap for etc. (deceive) 545.    ... show more