St. Louis Federal Reserve Bank President James Bullard said on Tuesday that public anger over the U.S. financial crisis and subsequent bailouts could cause big problems if this escalated into a political challenge to the independence of the U.S. central bank.

If that leads to some sort of erosion, or even the appearance of an erosion, of the independence of the Fed, I think that could be very counterproductive in this environment, he said after giving a talk about monetary policy to a Global Interdependence Center event.

The atmosphere between the Fed and the U.S. Congress has become very tense in the wake of last year's crisis. Lawmakers are angry over the taxpayer-backed rescues of investment bank Bear Stearns and insurer American International Group, which led to a public outcry that could hurt them in the polls.

Fed Chairman Ben Bernanke also endured a hostile congressional grilling last week over the Fed's role in Bank of America's purchase of Merrill Lynch, and lawmakers have demanded Fed emails and questioned its accountability.

All of this is taking place against the background of a record U.S. budget deficit, and an unprecedentedly aggressive Fed purchase program of U.S. government debt.

We've got very large fiscal deficits. We've got the appearance...that the Fed is monetizing the deficit, pushing up yields. Anything that is going to erode the independence of the Fed is going to feed that expectation and drive yields higher.

So I think we are really in a delicate situation here as regards the independence of the Fed, and that is an important consideration going forward, he said in response to a question from the audience.

Bullard said that he did not believe the Congress really wanted to clip the Fed's wings, but warned it would be easy for foreign investors to get the wrong message, and conclude that the Fed was going to finance the deficit by printing money.

The Congress has thought over the last 100 years about how much independence to give the central bank. And when they really think about it, at the end of the day, they want the level of independence that we have. And so I think that will be the end outcome of this, he told reporters.

I don't think anyone involved intends to monetize the debt, but that is what it looks like to outsiders, he said.

EXIT STRATEGY

In earlier remarks, Bullard said that the Fed's very accommodative monetary policy will remain in place for an extended period and a premature exit from this strategy could thwart U.S. economic recovery.

But Bullard said having a plan to shrink the monetary base after the Fed massively expanded it was important to control inflation expectations. And he said selling Fed-held assets was probably the most likely way it would choose to go.

Without an exit strategy, expectations of high inflation may develop, Bullard said at the event, which was held at the Federal Reserve Bank of Philadelphia.

If expectations of inflation feed into today's long-term yields, those yields will rise today and hamper recovery prospects, he said in prepared remarks.

He later told reporters that mapping out an exit strategy did not mean an imminent threat of rate hikes.

It is not that we are trying to back off accommodative monetary policy. Policy is very accommodative and it will remain accommodative. But you still have to map out what is going to happen in the future, he said.

Bullard will be a voting member of the Fed's policy-setting committee next year.

The Fed has cut interest rates to almost zero and pledged to buy up to $1.75 trillion worth of U.S. government and mortgage debt to combat a severe recession and prevent the economy from slipping into a Japan-style deflation, which inflicted a decade of stagnation on that country in the 1990s.

It left this purchase program in place and unchanged at its meeting last week, and Bullard said this reflected some recent improvements in the U.S. economic outlook.

I think the idea is to see how the data comes in over the summer here and then evaluate at that point, he said.

Bullard, in remarks used in a PowerPoint presentation to illustrate his argument, said there were various ways the Fed could reduce its balance sheet to tighten policy.

But he said two options -- the issuance of Treasury supplementary financing programs or the issuance of Fed debt -- were unlikely because of the size of the U.S. budget deficit.

Other options involving repurchase programs and the payment by the Fed of interest on reserves were untested in the context of the central banks's current operating environment, he said.

Selling assets as appropriate is the most likely option, he said.

(Reporting by Alister Bull; Editing by Andrea Ricci)