Will not stand up to examination, is unconvincing, will not work, as in That excuse about your sick aunt just won't wash. This expression originally alluded to a fabric that would not stand up to washing but by the late 1800s was used figuratively for other kinds of failure.
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Example sentences from the Web for won't wash
In 1992, Republican George H.W. Bush won the Asian-American vote by 24 points.
No Jewish woman has been crowned Miss America since Bess Myerson won in 1945.Why Was Bess Myerson the First and Last Jewish Miss America?|Emily Shire|January 7, 2015|DAILY BEAST
Several Republicans won primaries in 2014 by running as ideologically pure conservatives who wanted new leadership in the House.
And keep in mind that when Huckabee ran for president in 2008, he won the Iowa caucuses.
In a frightening development for the GOP, Democrats had won even traditionally Republican constituencies in the Midwest.
There'll be heaps uh fun in the Cypress Hills country when they get t' runnin' the whisky-jacks out.Raw Gold|Bertrand W. Sinclair
He stood before the glass hung above the wash bench and 369 smoothed his hair.The Bondboy|George W. (George Washington) Ogden
Then she won, and went half mad with the joy and excitement, but the joy didn't last long.Rosemary in Search of a Father|C. N. Williamson
An with that I laid down on the settee, an felt orful bad, an the more I tho't about it, the wus I felt.
But the nasty part of the whole thing was, that Haggard had won eleven thousand pounds from a weak-headed boy.The Pit Town Coronet, Volume I (of 3)|Charles James Wills