NEW YORK (CNN/Money) - President Bush's decision to back Alan Greenspan for another term as Federal Reserve chairman is certainly a good thing for the president's political future -- but is it good for the economy?

On Tuesday, any speculation that Greenspan's unkind words about Bush's tax-cut plans might have earned him a one-way ticket to Retirementville ended when Bush said he planned to reappoint the Fed chairman for another term after Greenspan's current term ends in June 2004.

Greenspan, who is recuperating from what the Fed called routine, successful surgery for an enlarged prostate, said Wednesday that he would agree to serve another term.

You don't have to be Karl Rove to realize that canning Greenspan, who's widely considered a "maestro" of economic policy, just months before the 2004 presidential election, would have been an enormous political blunder.

"With all Greenspan's capabilities, with his name recognition domestically and internationally, and with the stock market beginning to show some signs of life, the president wanted to get this out of the way," said Allen Jacobson, a political analyst with Washington Analysis. "He wants to be re-elected, and this is not the time to make any major changes."

Most people, from experts to CNN/Money readers, think this decision also was good for the U.S. economy, which still is struggling to recover fully from the recession of 2001.

In a poll taken on this Web site Tuesday and Wednesday, 69 percent of more than 22,500 respondents thought Greenspan, 77, should serve another term as chairman. And many Fed watchers and economists were vocal in their agreement.

"Not only is he as mentally acute as the average 77-year-old, he's as acute as the average 27-year-old. He has a phenomenal mind and very good judgment," said former Fed Governor Lyle Gramley, now a consulting economist with Schwab Washington Research Group. "People close to the decision-making at the Fed are almost unanimously in great praise of him, as I would be. I think it's a wonderful thing for the Fed and for the country that he's being kept on."

A few years ago, it would have been hard to find much disagreement with this view. People remembered Greenspan's deft handling of the 1987 stock-market crash and the 1997-98 Asian financial crisis, and certainly had little about which to complain, with stocks booming and unemployment and inflation low.

President Bush said he would back Federal Reserve Chairman Alan Greenspan for another term. CNNfn's Tim O'Brien reports. Play video (QuickTime, Real or Windows Media)

But in the wake of the bursting of the stock-market bubble in 2000, Greenspan's critics have grown more vocal, and some of the Teflon has been scraped from his reputation. Critics say he should have seen the bubble coming and done more to stop it, either by raising interest rates or using some of the market-regulating tools available to him.

He hasn't much helped his cause by being somewhat inconsistent in responding to these criticisms. He's said he couldn't have seen a bubble coming, though Fed records clearly indicate it was on his mind in the mid-1990s. He's also said there wasn't anything the Fed could have done about the bubble, though Fed records again show he and other officials discussed possible remedies.

"It's likely that markets and citizens and politicians will come to view Greenspan as less indispensable as time goes forward," said Thomas Schlesinger, executive director of the Financial Markets Center in Philomont, Va., a research group that studies the Fed, the nation's central bank. "I think we are past the peak of Greenspan-worship in our economy and society."

As Greenspan's luster dims, so could his credibility -- and his ability to manipulate markets and the economy.

Of course, this would be good news for those observers who think Greenspan hasn't done enough to discourage his cult of personality. In his closely watched Congressional testimony, for example, many critics wish he would decline to answer when lawmakers question him about tax policy and a host of other issues that really don't fall in his job description.

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"People called him clairvoyant, and he never said, 'Shucks, it's not me, it's the cycle -- I don't see around corners, and I never have,'" James Grant, editor of Grant's Interest Rate Observer, told CNN/Money last year.

Instead, he has weighed in on a wide variety of topics, most recently supporting a tax cut in 2001, but dismissing Bush's latest $726 billion tax-cut proposal, saying the economy didn't need it and warning it could wreck the budget.

Greenspan's support did much to encourage Congress to pass the 2001 tax cut, and his warnings about Bush's latest plan may have encouraged Congress to slash it in half.

That's all well and good if Greenspan was right in both instances -- but what if he gets the next call wrong?

"There's a risk to someone assuming this hero-type status because then there's the temptation you're going to lean toward believing him no matter what says -- and that's potentially dangerous," said Natexis Bleichroeder economist James Padinha.

For this reason, Padinha and some other economists wouldn't mind seeing the Fed run by somebody with a little less personality.

"I feel strongly that a ham sandwich with a scepter would be a fine Fed chairman," Padinha said. "In fact, I think a ham sandwich with a scepter might do a better job because it wouldn't be politically motivated."