It used to be easy to guess how many Americans would have problems paying their credit card bills. Banks just looked at unemployment: Fewer jobs meant more trouble ahead.

The unemployment rate has long mirrored banks’ loss rates on card balances. But Eddie Ward, 32 and jobless, may be one reason that rule of thumb no longer holds. For many lenders, losses are now starting to outpace layoffs.

Mr. Ward, of Arkansas, lost his job at a retail warehouse in April and so far has managed to make minimum payments on his credit card debt, which he estimates at $15,000 to $20,000. Asked whether he thinks he will be able to pay off his balance, he said, “Not unless I win the lottery.”

In the meantime, he said, “I’m just doing what I can.”

Experts predict that millions of Americans will not be able to pay off their debts, leaving a gaping hole at ailing banks still trying to recover from the housing bust.