Green’s Dictionary of Slang

(US) a general excl. of hostility or dismissal.

1906		Marvel 27 Oct. 391: ‘Suck eggs!’ said Finch shortly. ‘What’s the use of jawing?’.
1946		(con. 1912) B. Marshall George Brown’s Schooldays 71: You can tell your pater from me to go and suck eggs.
1982		P. Slabolepszy Sat. Night at the Palace (1985) 59: Well, stuff him. He can go suck eggs.
1987		B. Chatwin Songlines 74: I nodded to a woman who said, ‘Go and suck eggs!’.