This is supposed to be much bigger than the Target breach. If this doesn't give the move to the more secure EMV chip and pin method in the US, nothing will.
Having chipped cards would not prevent this. It would slow down criminals cloning cards but the numbers can still easily be used fraudulently online.
When you pay using the debit card, you have to insert the part of the card with the chip into a reader and enter your pin. Typically you can not do this until the cash register has transferred the amount to pay to the terminal.
You can also use it as a credit card when abroad or even in Norway. However, I'm not sure if the card will actually allow you credit (i.e. borrow money) per se -- I believe the account must have a sufficient positive balance, and I believe the domestic terminals are able to check that in real time (i.e. in a few seconds) and decline the sale if not funded.
As for online purchases, every time I use it as a credit card, I get re-routed to a card verification process. This means I get taken to some third party site (typically Visa or MasterCard) where I have to authenticate using my password and generate a one-time password (pin) on my phone. You can also use a FOB, but I find a phone more practical. After the verification is done, you get taken back to the merchant site. This is the same verification process that is used for online banking.
After living 15 years in the states I found this to be a bit annoying at first, but that had more to do with the speed of the implementation and the fact that it's applet-based (Java and Chrome -- have to switch browsers and hope that you don't lose your session).
If I had to authenticate every time I bought something on Amazon it would get old pretty fast. However, one could simply authenticate once to indicate that this merchant is trusted. A new merchant would trigger the authentication before the transaction can be accepted.