NEW YORK (CNN/Money) - For years, a lot of folks on Wall Street, and even on Main Street, have seemed to think that Fed chief Alan Greenspan walks on water. Now it looks like he's walking on thin ice, and he has no one to blame but himself.

On Tuesday Greenspan told Congress the economy does not need fiscal stimulus -- in plain English, it doesn't need tax cuts or other measures. This was widely seen as a big slap in the face to President Bush, whose huge fiscal stimulus plan hinges on the notion that the economy is in danger of sinking.

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I was at the hearing. I did not get the feeling that Greenspan was "going after" Bush's plan. After all, he did endorse, as he has in the past, eliminating the tax on stock dividends, the keystone of the president's plan. He also said that the White House plan has "pluses and minuses," certainly a nice equivocal and vague assessment.

But this is the Federal Reserve chairman! He knows that every word he says echoes around the world, around the markets, around the hallways of Washington.

And he realizes better than anyone that for head of the Federal Reserve to go beyond matters of monetary policy (interest rates, money supply, bank credit) is dangerous.

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Hard to argue with Republican Senator Jim Bunning: "No president should try to set monetary policy," Bunning told Greenspan at Tuesday's hearing. "But the Fed chairman should not try to make fiscal policy. That's not your job."

Consider Greenspan's predecessor, Paul Volcker. When Volcker led the Fed he meticulously avoided getting dragged into discussions in which he would have to comment on specific fiscal policy matters.

Volcker did, however, argue constantly and consistently that the growing budget deficit of the 1980's was a big problem for the economy. A bigger deficit "crowded out" private investors, because more government borrowing left less credit available for businesses to borrow. And, it meant a higher cost of borrowing, i.e., higher interest rates, than would otherwise have existed. It was a like a mantra for him.

Greenspan rightfully, and appropriately, is arguing now that a growing budget deficit does affect interest rates and the economy, and that if the deficit gets too big there will be no way the economy can grow fast enough to get rid of it -- contrary to prominent "supply-side" economists and Republicans who say that tax cuts will boost growth, and that faster growth will lead to rising tax revenues that will whittle down the deficit.

But remember two years ago when Greenspan shocked a lot of folks in Washington and Wall Street by coming out and arguing that Congress needed to cut taxes because the budget surplus was so big it was a threat to the economy? This was just about the time that President Bush was starting to push for tax cuts, so it was viewed as an overtly political statement by a Fed chairman that everyone knows happens to be a Republican.

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Call me naïve, but I believed Greenspan made those remarks because he believed them, not because he was trying to help Bush. And many economists have defended Greenspan's view, saying there was no way to know that the extraordinary of rate of growth of tax revenues would not continue (even though many were puzzled as to what was causing the rapid growth and therefore wondering how long it would last).

But Mr. G. would never have gotten into any kind of trouble or stirred up any kind of controversy if he had just stayed out of the matter. He doesn't HAVE to talk about fiscal policy. He doesn't NEED to discuss tax policy.

The Federal Reserve is an independent body because Congress wisely decided that monetary policy should be independent of politics. Think about it. When the economy is weak what president or political party would NOT want to kick things up by cutting rates aggressively, even if it risked rising inflation?

The more the head of the Fed, especially one as powerful as Alan Greenspan, meddles in matters the politicians control, the more he opens up the central bank to criticisms that IT has become political. And that's the last thing the Fed needs.

Kathleen Hays co-anchors Money & Markets, airing Monday to Friday on CNNfn, and appears throughout the day reporting on the economy and how it affects financial markets. As part of CNN's Business News team, she is also a regular contributor to Lou Dobbs Moneyline.