Green’s Dictionary of Slang

being inattentive, not concentrating on a task.

1957		‘Ed Lacy’ Lead With Your Left (1958) 35: Asleep at the wheel, wonder boy?
2000		Federal Computer Week mag. 15 Feb. n.p.: Ira Winkler, [...] said electronic enterprises are ‘asleep at the wheel’ when it comes to Internet security. ‘For every one thing they know about, there’s a dozen things they don’t know.’.