The Federal Reserve decided last weekend in the inferno of the financial crisis that Wall Street’s major players — even a smallish and brutish one, Bear Stearns — are too big to fail. So the Fed is pumping all-but-unlimited amounts of all-but-free money into the financial system to keep it operating despite the Wall Street bank run.

But is the Fed itself too big to fail? And what institution would step in as the buyer of last, last resort — if the buyer of last resort should prove insufficient to the challenge?

Our instinctive response is to say this scenario is implausible. The Federal Reserve reflects “the full faith and credit” of America, in the time-honored phrase. The very idea that the Fed couldn’t meet its obligations is unthinkable. So, not surprisingly, Wall Street’s reaction to the Fed’s rescue mission has been a shout of joy.

The Fed’s feel-good strategy continued on Tuesday, when the central bank cut the federal funds rate three-quarters of a point to 2.25% — almost a fire sale on money — which helped push the Dow Jones industrial average up a thumping 420 points.

But let’s think for a moment about the unthinkable. Given the Fed’s failure over the past nine months to stem the mounting fear in the market, and given the enormity of the correction in the housing market that’s still ahead, you have to ask what’s next if this week’s rescue measures aren’t successful.

The danger is acute because the financial crisis is moving to Main Street from Wall Street. So far, the panic has been confined to people in the financial world who understood the exotic securities that were imploding and knew just how bad the credit crisis was. Now we’re entering a new phase, where Mom and Pop will be losing their homes, and maybe their jobs — and the public will be getting plenty scared.

We speak about the current meltdown as the “subprime crisis,” as if it were simply the product of imprudent loans by greedy financial concerns — and certainly there’s been a lot of that. But the larger dynamic is that the bubble in the housing market has burst. That’s why subprime loans became worthless and why the daisy chain of mortgage-backed securities has unraveled.

The former Fed chairman whom many blame for the housing bubble, Alan Greenspan, made this point in a stunningly unapologetic article in Monday’s Financial Times. After predicting that the financial crisis will be “the most wrenching since the end of the Second World War,” he warned that it won’t end until home prices stabilize.

A prominent investment banker offers a helpful, if also somewhat terrifying, explanation of what may be ahead. The Fed has pledged itself to a rescue package whose ultimate scope is unknown but that will put at risk the nation’s most precious asset, which is the Fed’s credibility.

How much bad debt will the Fed have to assume? Nobody knows. Estimates of the subprime portion range up to $400 billion, but that’s just the beginning. The consensus among analysts is that losses in credit markets will total at least $600 billion, but suppose it proves to be double that, or triple?

“It’s not a liquidity crisis, but a solvency crisis,” my banker friend says. “Can the Fed really take on $1 trillion of impaired securities? $2 trillion? More?” The takeover of the savings-and-loan industry by Resolution Trust Corp. in the early 1990s was relatively small in comparison, a mere $250 billion in current dollars, and the assets the RTC acquired were easily quantifiable, unlike today’s mess of sliced-and-diced securitized mortgages.

Think about what’s ahead as the housing bubble continues to contract. How big a drain will that be? The American residential mortgage market is about $12 trillion, and the overall value of the housing market is about $20 trillion. Many analysts predict that this market will fall 20% further before it bottoms out. That would be a loss of $4 trillion in value in an economy whose gross domestic product last year was about $14.1 trillion.

In this post-bubble economy, we would see waves of panic selling — not by Wall Street fat cats but by frightened homeowners trying to repay crushing mortgage debt, by angry workers who have lost their jobs, by people desperate to pay their bills.

The Fed, in my view, had no choice but to step in decisively this week and try to stop the Wall Street bank run. But when the panic hits Main Street, the Fed will have to be even more creative — in fashioning a package that restores confidence but also allows real estate prices to fall and the market to clear.

Coping with the worst financial crisis since the Great Depression will require the best financial minds since that time. What we have is a lame-duck president, election-year politicking, and a Fed that has been bold and innovative, but whose reach may have exceeded its grasp.