I'm going the last 5 days w/o coffee and felt no difference at all regarding anxiety, focus, sleep & headaches. I normally drank 3 cups in the morning (200ml each I'd guess) and 3 after lunch.
Caffeine sensitivity is highly variable between individuals. I am both sensitive and a slow metabolizer; if I had 6 cups of coffee in one day my guts would be churning and I would not be able to get anything done.