Republicans in Congress have lots of ideas of their own for expanding the tax package, including a reduction in the capital gains tax, the addition of provisions favoring businesses, and expansions of the individual retirement account and 401(k) retirement savings plans. And the administration is close to a decision to speed up the tax cut by reducing income tax withholding this year, a development reported today by The Wall Street Journal.

''Greenspan probably has more impact on the fate of a tax cut than the president of the United States,'' said Mark A. Bloomfield, president of the American Council for Capital Formation, a business-financed group that lobbies for tax cuts.

For Mr. Bush, whose father's administration had strained and at times hostile relations with Mr. Greenspan, the Fed chairman's stance on taxes held the promise of a more productive partnership. Mr. Bush's Treasury secretary, Paul H. O'Neill, has already signaled that he shares Mr. Greenspan's views on economic policy.

Among Democrats, though, there was a sense of disappointment, and some suspicion that after eight years with a Democrat in the White House Mr. Greenspan was revealing his true colors as a conservative whose ties to Republican politics date to Richard M. Nixon's 1968 campaign.

To them, Mr. Greenspan had been a bulwark against fiscal irresponsibility. By opening the door to a large tax cut, they said, Mr. Greenspan was inviting a bidding war that could lead to a tax reduction so big that it could threaten the government's newfound fiscal health just as it is confronting the rising costs of providing retirement and health benefits to the baby boom generation.

''He's taken the lid off the punch bowl,'' said Senator Paul S. Sarbanes, Democrat of Maryland. ''And once you take the lid off the punch bowl, you can't say you can only have half a cup.''

So distressed were Democrats that some of them said Mr. Greenspan might have hurt his standing among them. While they acknowledged that it was fruitless for them to fight the Fed chairman publicly, some of them said privately that he would receive less deference on Capitol Hill in the future.