Green’s Dictionary of Slang

(US, esp. Southern) to be mean and irritable; to be overbearing and unpleasant; of a situation, to be reprehensible, e.g. that sucks eggs.

1903		A. Adams Log of a Cowboy 39: A few doses like that will cure him of sucking eggs and acting smart, interrupting folks.
1912		Eve. Star (Independence, KS) 30 July 2/3: Curtis lined up [...] with the same crowd he lines up with at home — the reactionaries who try to fool the people [...] Curtis then voted against it [...] That is what you call sucking eggs and hiding the shells.
1930		D.M. Garrison ‘Song of the Pipeline’ in Botkin Folk-Say 110: Gawd, that broke me from sucking eggs.
1934		Z.N. Hurston Jonah’s Gourd Vine (1995) 43: You come grab me now and Ah bet yuh Ah’ll stop you from suckin’ eggs.
1942		Montgomery Advertiser (AL) 15 May 4/2: Occasionally one of the brothers catch one of theirnumber ‘sucking eggs’.
1986		Chapman NDAS.