There’s good news and bad news in the FDIC’s quarterly profile of the banking sector. The good news is that FDIC has more resources than you think to handle the problem banks on its radar. The bad news is that the too-big-to-fail banks aren’t on it.

The balance in the FDIC’s deposit insurance fund ended the quarter at $10.4 billion — its lowest since the savings and loan debacle — but it isn’t the only security blanket protecting insured depositors. The agency also has a “contingent loss reserve.”

If you add the loss reserve to the deposit insurance fund balance, the FDIC’s total resources were $42 billion at the end of the second quarter. Despite 24 bank failures during the quarter, that total actually increased by half a billion dollars.

How could that be? The biggest reason is that the FDIC is finally getting serious about charging premiums for the insurance it provides. Member banks were charged $9.1 billion to replenish the fund last quarter. That’s up from $2.6 billion in the first quarter and $640 million a year ago.

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A similar amount may be raised this quarter if the agency charges banks another “special assessment.” While that decision won’t be made till next month, it looks likely. That’s great news for taxpayers who would otherwise have to plug the hole if the FDIC runs out of money.

Banks complain that special assessments put too much pressure on them at a tough time. But it’s their own fault the deposit insurance fund is running so low.

According to a Boston Globe article by Michael Kranish earlier this year, about 95 percent of banks paid nothing for their deposit insurance from 1996-2006. But that wasn’t FDIC’s fault; they were prevented by law from charging premiums. Congress didn’t think it was necessary. Oops.

So the deposit insurance fund will be under pressure for some time. FDIC’s problem bank list grew to 416 at the end of last quarter. These banks have $300 billion of assets.

In total, FDIC estimates the banking sector is wrestling with $332 billion worth of loans and leases on which borrowers have stopped making payments. That excludes hundreds of billions worth of underwater loans that may be current now but will ultimately default. Many banks, including the largest ones, are likely to struggle for some time.

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And that’s the bigger story here. Citigroup and Bank of America have received hundreds of billions of dollars of government support, but, precisely because of that support, they’re not on the FDIC’s list. Adding them to it would multiply total problem assets 10 times, to $3 trillion.

Overall, the deposit insurance fund is tiny compared with the total amount of deposits that are insured. The official total is $4.8 trillion, but that excludes “temporary” increases in deposit insurance instituted last fall.

One program, which increased insurance limits to $250,000 for individuals, now backs $725 billion of deposits. Earlier this year it was extended to 2013. The other program, which provides unlimited insurance coverage for transaction accounts, backs $736 billion of deposits. On Wednesday, that program was extended through June of next year.

Add those amounts to the official figure and you have the real total: $6.3 trillion, huge relative to the resources of the insurance fund.

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Asset prices aren’t going back to their highs of 2006-2007, so loans held against them will be generating losses for years. The FDIC may raise enough cash from banks to fund depositor losses in small and medium-sized banks, but it is clear that the biggest banks are far too large for them to handle.

As a result, the government’s emergency rescue measures aren’t going away for a while. And taxpayers should expect to be writing fat bailout checks to the financial system for years to come.