"ineffectual," 1932; "Dictionary of American Slang" suggests it is perhaps a humorous mispronunciation of haphazard. Compare half-hearted.
Entries linking to half-assed
haphazard adj.
"characterized by randomness, chance, accidental," 1670s, from noun meaning "a chance, accident" (1570s), from hap (n.) "chance, luck" + hazard (n.) "risk, danger, peril." Related: Haphazardly.
half-hearted adj.
also halfhearted, "showing little enthusiasm," early 15c.; see half + -hearted. Related: halfheartedly; halfheartedness. English in 17c. had also half-headed "stupid."