could give a damn/couldn’t give a damn
If you don’t care at all about something, the standard popular expression is “I couldn’t give a damn.” People often say instead “I could give a damn,” which should logically mean they care. Note that we say “I don’t give a damn,” not “I give a damn” unless it’s set in some kind of negative context such as “do you really think I give a damn?” or “do I look like I give a damn?’
The same goes for parallel expressions where the last word is “darn” or some other expletive.
Just remember that in Gone with the Wind Clark Gable told Vivien Leigh, “Frankly, my dear, I don’t give a damn.”
The new edition of Common Errors in English Usage is now shipping,
and it makes a great gift. When you order 5–9 copies and use the coupon
code FIFTEEN, you pay only $13.48 each. Order 10 or more for just
$12.15 each. All with free shipping in the US. Single-copy shoppers can
still use the coupon code and get the new edition for $15.