I've never had a checking account compromise, but I'm pretty sure it would be a massive pain in the ass by comparison.
A compromise of your routing and account number for your checking account is potentially much worse. It's harder to take advantage of, but it's also much harder to fix.
(I'm not sure if you were treating the debit card as analogous to credit cards or account numbers, so treat this as confirmation/correction/elaboration/whatever as appropriate.)
From what I recall with the Target incident, their cost is something like $2-5 for each replacement card, so it's not entirely trivial. If you requested a new one on a regular basis for no good reason, they might put a stop to it one way or another.
As far as peace of mind goes, since the consequences are so mild, I wouldn't worry about it.
Checking account info is much, much worse. It's much harder to reverse fraudulent transactions there, and much harder to get a new number.