Come to someone in great numbers, as in Ever since she appeared on television, agents have been beating a path to her door. The term beat a path alludes to the trampling action of many feet. [Late 1500s]
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.