Bandwidth
Personal capacity, borrowed from networking hardware. Saying 'I don't have the bandwidth' is the polite, machine-flavored way of saying 'no' without saying no.
Heard in the wild
“I'd love to help with the deck, but I don't have the bandwidth this week.”
Tone check: Cliché
Cliché, but socially useful. It's the most acceptable 'no' in corporate English.