It sounds like a long shot, but New York City Comptroller John Liu (right) is willing to give it a try. Liu leads a group of public pension fund managers in five states who released a letter Sunday demanding the banks investigate their mortgage and foreclosure practices.

The letters went to Bank of America (BAC), JPMorgan Chase (JPM), Wells Fargo (WFC) and Citigroup (C). Liu’s group includes state retirement funds in Connecticut, Illinois, North Carolina and Oregon and has $432 billion in assets.

The campaign is nothing if not well timed. On Friday, bank stocks tumbled after a Massachusetts court ruled two 2007 foreclosures invalid on the grounds the banks couldn’t prove they owned the mortgages. One justice blasted Wells and U.S. Bancorp (USB) for their “utter carelessness” in handling homeownership documents.

“The banks’ boards cannot continue to pretend the foreclosure mess is the result of technical glitches and paperwork errors,” Liu said.

That remains to be seen, alas. The banks didn’t exactly beat a path to Liu’s doorstep to ask how they might stay in the pension funds’ good graces, in spite of the $5.7 billion the funds have invested in the banks. That sounds like a lot, but it’s a rounding error next to the big four’s combined market value of $625 billion.

Citi and Wells Fargo both said they are reviewing the letter from the state pension funds. JPMorgan Chase declined to comment. Update 9 a.m.: Bank of America said:

The letter from the pension funds brings up a concern that the bank is already addressing – the future prevention of compliance failures and restoration of confidence in the foreclosure processes. The points they make have been brought up time and time again, reviewed and fully considered. In fact, this week, the bank filed a brief in response to a New Jersey judge that essentially addresses the same concerns.

This is no surprise, of course. For the past four months, reports of shoddy practices ranging from robosigning to parrot theft have made a mockery of the notion that the banks are interested in anything but the bottom line.

Yet the the bankers have continued to sidestep the issue, and their greed and irresponsibility have yet to become anything approaching a bipartisan issue in Washington. The new chairman of the House Financial Services Committee, Rep. Spencer Bachus of Alabama, recently sized up the government’s job as doing what it can to help the banks.

Meanwhile, the White House appears intent on using taxpayer-backed Fannie Mae and Freddie Mac to soak up the risk that another housing downturn will hammer bank balance sheets. Favorable settlements will only strengthen bankers such as BofA chief Brian Moynihan, who last year likened the bank’s relationship with mortgage investors to hand to hand combat.

Fortifying the already entrenched bankers won’t make fixing the troubled U.S. financial system any easier. The mortgage securities market could be vulnerable to rulings like the one in Massachusetts Friday, because investors may eventually decide the banks’ promises simply aren’t trustworthy.

“This is a landmark case that goes to the heart of the securitization industry,” said Susan Wachter, a real estate and finance professor at Penn’s Wharton School in Philadelphia . “The real message is that this system is broken, and we are going to need to find a way to rebuild it.”

Liu, a Democrat, has tried to appeal to the bankers’ better side before, to no avail. In November, he filed shareholder proposals at the four banks calling for a shareholder vote on an audit of mortgage practices. He said at a conference last fall that the banks must prove they are acting responsibly before the economy will recover.

“Foreclosuregate probably isn’t the end of the world, but it’s pretty bad,” he said in October. “If public confidence isn’t there, the foundation of the whole financial system is shaken.”

But the message of the past year is that the bankers don’t care what’s shaking as long as their jobs are secure — and there’s not much the pension funds can do about that.