I used a Barclay card at Target during the affected time frame. They're basically taking the same position as Chase in the post above. They're well aware of the issue so unless I see a fraudulent charge I'm not going to panic. Perhaps I'm being naive but I use and watch the card frequently so I'm confident I'll notice if anything strange shows up.
I thought I had also used my debit card, and that had me worried. But I checked my account and turns out I was wrong. It was KMart. I always mix those stores up in my mind, in fact on the day in question I'm pretty sure I first drove to Target by accident.
This situation does make me glad that I switched to using credit cards instead of using my debit everywhere. The reason I used the debit at KMart was because of a temporary offer that showed up on that account.