teeter on the brink of (something)
To be very close to doing something or of having some imminent event happen, especially that which is bad or disastrous. The company is still doing business, but ever since the recession hit, they've been teetering on the brink of closing down. The crew are so maddened by the cuts to their pay that everyone is teetering on the brink of mutiny.
teeter on the brink (or edge)
be very close to a difficult or dangerous situation. 1997 James Ryan Dismantling Mr Doyle Letting her secret teeter on the brink of becoming public was a game Eve played more and more.