Refuse to go any further than, as in I draw the line at giving them more money. This expression alludes to a line drawn at a stopping point of some kind. [Late 1700s]
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.