on/to the verge of something/of doing something
on the verge of (something)
Very closely approaching something; very nearly at the point at which something will happen. After weeks of failed experiments, I think we're finally on the verge of a breakthrough.
to the verge of (something)
To the cusp of something; to the point where some action or outcome is nearly able to happen. Their latest victory pushes this underdog team to the verge of the playoffs for the first time in over 60 years. The civil war has pushed the country to the verge of total famine.
on the verge of
Close to, on the brink of, as in I was on the verge of calling the doctor when he suddenly got better, or Sara was on the verge of tears when she heard the news. This term uses verge in the sense of "the brink or border of something." [Mid-1800s]