Green’s Dictionary of Slang

(US) as an intensive, enormous.

1854		M.J. Holmes Tempest and Sunshine 93: Tell her there’s heaps of folks here, and mind tell Judy to get us up a whalin dinner.
1893		F.P. Dunne in Schaaf Mr Dooley’s Chicago (1977) 53: It always looked like a whaling big lie to me.
1909		L.W. Payne Jr ‘Word-List From East Alabama’ in DN III:v 387: whalin(g), adj. Surprisingly large, whopping.
1912		Van Loan ‘Little Sunset’ in Ten-Thousand-Dollar Arm 90: What a whaling great infielder he’ll make some day.