A bad egg

The allusion is clearly to the disappointment felt when cracking or shelling an egg, only to find that it is bad. The earliest use of the phrase in that context that I have found is in the Milwaukee Daily American, September 1856:

“Mayor Wood is moving heaven and earth to procure his renomination. One of his dodges is, to get up letters in the newspaper, pretending to emanate from ‘distinguished citizens,’ including merchants, mechanics and working men, soliciting him in the most pathetic terms to present himself to the dear people. There are also on the list a number of notorious blacklegs whom Woods keeps in pay. He is a bad egg.”

See also, ‘the Curate’s egg‘.