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]

The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Company. All rights reserved.