Green’s Dictionary of Slang

(US) despicable, foolish; esp. as suck-egg dog/hound.

1851		‘How Mike Hooter Came Very Near “Wolloping” Arch Coony’ in T.A. Burke Polly Peablossom’s Wedding 153: You eternal, yaller-faced, pisen-mouthed, suck-egg son of er ---!
1887		in Overland Monthly (CA) July 67: Tom Welsh air er nasty, weevul-eatin’, suck-aig hound.
1892		J.C. Duval Adventures of Jack Dobell 99: These dogs were not mongrels or ‘curs of low degree,’ neither were they of the ‘suck egg’ breed.
1909		L.W. Payne Jr ‘Word-List From East Alabama’ in DN III:v 377: suck-egg, adj. Egg-sucking. ‘I’ll have to kill that old suck-egg dog.’.
1922		(con. late 19C) A. Gonzales Black Border 33: Joe look shameface’ ez uh suck-aig dog.
1926		Z.N. Hurston Sweat (1995) 963: Ah hates yuh lak uh suck-egg dog.
1932		J. Peterkin Bright Skin 131: Blue acted shamefaced as a suck-egg dog.
1946		H.A. Smith Rhubarb 41: ‘I be a suck-egg mule,’ he finally said.
1949		(con. 1943–5) A. Murphy To Hell and Back (1950) 198: ‘Well, I’ll be a suck-aig mule,’ says Snuffy.
1972		(con. 1916) G. Swarthout Tin Lizzie Troop (1978) 83: I’ll be a suck-egg mule, thought Stanley Dinkle.
1983		J. Ciardi A Second Browser’s Dict. 192: Mule: suck-egg mule. A nonesuch idiom [...] Well, I’ll be a suck-egg mule! Exclam. of surprise, vexation.
1985		Columbia Journalism Rev. 8 July n.p.: Your newspaper is a suck-egg mule [R].