Tim Geithner: Is second time the charm? (Paul J. Richards/AFP/Getty)

The American public rightly is skeptical about the way the first $350 billion in Troubled Assets Relief Program funds were spent. Now comes the Obama administration with a new name for the second half of TARP spending — it’s part of a much grander Financial Stability Program — and a vow to increase its transparency and accountability.

Good steps, sure, but the $64 question — which actually could be a $2 trillion question — is will it work?

Will a public-private partnership to buy toxic assets directly from banks work better than throwing money at the banks and hoping they spend it wisely? For that matter, will the “private” half of the public-private partnership show up?

How will these assets — largely credit obligations on mortgage securities — be valued? The original mortgages have been monetized, securitized and tranched over and over again, making it almost impossible to determine what they’re worth. If the Treasury Department and the Federal Reserve, which will manage the program, pay too much for them, the taxpayers might never see a return. If Treasury and the Fed pay too little, banks may choose to hold onto them, for fear of having to raise too much capital to offset their losses.

Details of the new plan were in short supply on Tuesday, when Treasury Secretary Timothy F. Geithner announced the new program. Wall Street’s first reaction was negative with the Dow Jones industrial average closing down 382 points (4.6 percent) at 7,888.

Best guess: Treasury and Fed will overpay, at least at first, and critics won’t be much happier with Son of TARP than they were with TARP. But there’s really no way to avoid the problem. The government simply must get the credit markets thawed, and the best way to do that is to get all those lousy assets off banks’ balance sheets.

But that doesn’t immediately address those at the bottom of the food chain, homeowners stuck with mortgages they can’t pay. On Tuesday, President Barack Obama pitched his economic stimulus plan in Fort Myers, seat of Lee County, Fla., which has a 12 percent foreclosure rate, the highest in the nation.

The president said the $838 billion stimulus plan, passed by the Senate 61-37 as he arrived in Florida, combined with the Financial Stability Plan and other measures announced by Mr. Geithner, could help break the “vicious cycle” of the recession.

We certainly hope so. But Son of TARP may suffer, albeit in a lesser degree than TARP, from a serious deficiency: Too much dependence on a banking industry whose interests may not precisely coincide with the public’s. We would like to have seen government insist on a bigger role, rather than continuing to rely on the good offices of an industry that helped to create this crisis.

Some of Mr. Obama’s aides reportedly wanted to use a stick instead of a carrot, but Mr. Geithner — the former chairman of the New York Fed — argued that a harder line would be counterproductive. He believes the government’s proper role is to “help leverage private capital to help get private markets working again.”

So in addition to using the Fed’s balance sheet to take bad loans off bankers’ books — in effect, financing it with debt — the Treasury will spend most of the funds remaining from the original TARP program to unfreeze the market for commercial paper, car loans, student loans and credit card debt. A third component, a $50 billion mortgage-relief program, is set for announcement next week.

Mr. Obama and Mr. Geithner hope accountability rules and transparency — transactions will made public at FinancialStability.gov — will keep this round of spending from disappearing into a black hole.

But the burden now falls on financial industry executives: Mr. Obama and Mr. Geithner have given them one last shot. They can either go along with the program or risk the kind of public outrage that would begin the nationalization of banks. For that is surely the next step.