William Miller, the widely praised new chairman of the Federal Reserve Board, has made a potentially serious tactical blunder by seeming to reverse his stand on a touchy tax question because of Carter administration pressure.

At issue is Wisconsin Republican Rep. William Steiger's popular proposal to roll back capital-gains taxation to 1969 levels, now the business world's No. 1 legislative target. In private sessions with Republican congressmen and business representatives, Miller gave the distinct impression of supporting the Steiger amendment or at least its concept. Soon afterward, following arguments by Treasury Secretary W. Michael Blumenthal, Miller publicly opposed it.

Miller's position on the Stelger amendment is scarcely a matter of life or death, either for him or the amendment. What could be deadly are doubts Miller has generated among congressmen and businessmen about his own credibility, an indispensable asset for the nation's central banker.

Equally important is what the incident shows to businessmen, here and abroad, about Miller's ability to run the Fed independently of administration pressure. Since taking over from Arthur Burns March 8, Miller has energetically demonstrated independence from President Carter by word and deed. Those demonstrations are now undercut by Millers handling of the Steiger amendment.

On April 21 Miller received James Davidson of the National Taxpayers Union at the Fed. With Davidson was Richard Rahn of the American Council for Capital Formation, an organization beating the drums for the Steiger amendment. The two pushed Miller to get behind the amendment.

Without flatly endorsing the proposal, Miller left little doubt with Davidson and Rahn that he liked the idea and believed it would generate more tax revenues by stimulating economic activity. "I was sure he would give it favorable consideration," Davidson told us.

The happy word sped through business and congressional grapevines for two weeks, leading to Miller's May 3 appearance at the weekly off-the-record breakfast of the SOS club, an influential group of Republican congressmen. Steiger himself asked about the capital-gains question, and others chimed in.

Again, those present got the distinct impression that Miller was backing lower taxation of capital gains in general and the Steiger amendment in particular.

It was therefore with some shock that Rep. Barber Conable of New York, the Ways and Means Committee's senior Republican and a participant in the SOS breakfast, received a lefter from Miller dated May 5 unequivocally opposing the Steiger amendment. The conclusion among the SOS members, quickly spread by word of mouth, was that the administration has talked the chairman of the Fed into opposing what the president regards as a cancer on his tax program.

Through a spokesman, Miller informed us he never endorsed the amendment and was never even called upon to discuss that specific proposal - a claim at variance with several other accounts of the April 21 and May 3 meetings. Miller also said, according to the spokesman, that he had not discussed the Steiger amendment with "anybody in the government other than congressmen."

In fact, however, Blumenthal and Miller have talked over the Steiger amendment - definitely at their weekly breakfasts and perhaps on other occasions. While bending over backwards to insist he did not turn Miller around, Blumenthal acknowledges he argued against the Steiger amendment over the breakfast table - tacit admission that at one point Miller was much friendlier to the proposal than he is today.

Reactions to all this are mixed. "I'm disappointed," a terse Steiger told us. The Taxpayer Union's Davidson chooses to believe Miller in his heart favors the capital-gains rollback "no matter what he says in the letter [to Conable]." Other influential business leaders are deeply worried over the implications about Miller's credibility.

While White House aides and other administration officials are publicly unhappy over Miller's conservative anti-inflation rhetoric, they privately advise he is probably just appeasing his business constituency and will end up as a loyal member of the Carter team. Precisely that fear is secretly expressed by some of Miller's fellow governors on the Fed. Their apprehensions were stoked by the current Business Week's account of "the new Miller-Carter economic accord."

That is why Miller's blooper on the Steiger amendment is most untimely. His admirers have been saying that ex-industrialist Miller reflects the razorsharp intellect of Robert S. McNamara, but with political know-how that McNamara lacked. The second half of that description now seems in doubt.