That estimate is based on feedback the association has received so far from discussions with its 33 member banks, according to Jerry Little, president of the NHBA.

So far, 11 banks have reported being contacted by credit card companies about compromised card use, Little said. But indications are that all of NHBA's members have been affected by the breach, he said. The association has sent a survey to all its members and will have a better estimate of the financial fallout by early next week.

The banks that have reported in so far "have had significant compromises," Little said.

It's been a more difficult to get a handle on the extent to which the compromised cards are being used in fraudulent transactions, he said. But a few of the banks have reported fraudulent use of cards that are on the list of cards compromised in the TJX breach, and in some cases, the fraud appears to have been going on even before the breach was disclosed by TJX last week, he said.

It is still too early to say what the NHBA's response will be to the incident, Little said. But the group is considering options that include legal action against TJX and a push for legislative reform that would hold breached entities financially liable for the costs associated with blocking and reissuing credit and debit cards, he said.