Target is trying to get back in its customers' good graces after a massive data breach affecting some 40 million credit and debit account holders. The giant retail chain offered its customers a 10 percent discount over the weekend as an act of atonement, but business was said to be down anyway.

The breach affected customers who used their credit and debit cards at one of Target's 1,750 stores during a three-week period after Thanksgiving.

Brian Krebs, who broke the story in his cybersecurity blog, says he has already found evidence that some of these cards are being sold illegally online.

"It's clear that a large chunk, if not all of these cards, are being pushed out into the underground market. The question is: How much can the criminal community absorb?" Krebs asked.

Over the weekend, JPMorgan Chase limited the amount of cash withdrawals by customers who had shopped at Target in recent weeks. And it opened some of its branches to help customers deal with the problem. It did so even though Target says there's no evidence the hackers acquired customer PINs, which means they couldn't use Chase ATMs anyway.

Target tried to assure its customers that they will have zero liability for charges they didn't authorize, and it offered a discount to lure them back into the store.

Outside a Target in Washington, D.C., customer David Walsh wasn't too impressed: "They had a massive screw-up which could cause 40 million people to have some form of identity theft. A 10 percent discount over the holidays, it's a gesture; I don't know if it's enough of a gesture."

Customer Alexandra Neustadt says the incident has made her think twice about the way she shops.

"It does make you kind of think you should check your credit card statements. Maybe not do so many transactions on credit cards that are in different stores, different locations, online. I just use it as if it's nothing, and I think I need to pay more attention," she says.

Meanwhile, Target's Facebook page had plenty of scathing comments from customers whose accounts have been compromised, or who were unable to use their Chase debit cards because of the bank's restrictions.

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