When a customer cries, “ASAP!”, relax.
Because that’s not a deadline.
ASAP is uncomfortable because it’s ill-defined. Some focus on the “as soon as” part of it, others on “as possible” part. One is tense, one is slack. That’s not a deadline.
ASAP is uncomfortable because you’re anxious about the wrong thing. About getting something done “right this second”, rather than getting a workable deadline (date & time).
ASAP is what happens when deadlines don’t happen, but the thing still needed to get done, and still nobody stepped up to set a deadline.
So set a deadline.