I hope they catch whoever did this and make an example of them. Fraud of any kind affects all of us with higher prices.
That said, I have no qualms using my credit card anyplace. And yes, I have a Target card and shopped there during the affected dates. Most card companies these days are on top of fraud. I've had them call me to question a purchase and several times have had them send replacement cards due to a security breach (even though my card didn't appear to be affected).
My first brush with cc card theft happened with Discover. My bill had a slew of fraudulent purchases. They asked if I had any idea how my info had been stolen, took all the false charges off my bill with no hassle, and issued a new card.
A debit card is another matter entirely. I would NEVER use a debit card, because if that info is stolen the thief is able to empty money directly from your bank account. And I think that getting that squared away could be extremely difficult.