without a leg to stand on - Phrases/Idioms
The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 2003, 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
With no chance of success, as in He tried to get the town to change the street lights, but because there was no money in the budget he found himself without a leg to stand on. A related idiom is not have a leg to stand on, as in Once the detective exposed his false alibi, he didn't have a leg to stand on. This metaphoric idiom transfers lack of physical support to arguments or theories. [Late 1500s]