President Reagan, facing a deepening fiscal impasse in Congress, yesterday nominated Federal Trade Commission Chairman James C. Miller III to succeed David A. Stockman as director of the Office of Management and Budget.

In contrast to Stockman, who had advocated tax increases as well as spending cuts to reduce the deficit, Miller said recently that he thinks tax increases could hinder the economy and be "counterproductive."

The Miller nomination comes as the White House is girding for a possible confrontation over spending with Congress in the next few months. But Miller may not be confirmed by the Senate until September.

White House officials said yesterday that OMB Deputy Director Joseph R. Wright Jr. would fill the post in the interim. Stockman leaves office Aug. 1.

Differences between the House, the Senate and the White House have stalled the effort to write a congressional budget resolution slicing more than $50 billion off next year's deficit of about $200 billion.

Should that impasse persist, Congress will vote individual appropriations bills that could confront Reagan with difficult veto decisions, and possibly another battle over a continuing resolution of interim funding.

Already, the White House has labeled as "unacceptable" two spending bills that the House passed, and objected to four others awaiting floor action.

In the past, Stockman was able to negotiate agreements that made spending bills satisfactory to the White House, sparing Reagan a veto fight, but now the administration has lost its chief negotiator.

White House officials said they are also worried that a spending confrontation could increase pressure on Capitol Hill to use Reagan's tax overhaul proposal to raise more revenue.

Congress may also become ensnarled in another effort to raise the federal debt ceiling -- now at about $1.8 trillion before the 1986 fiscal year begins Oct. 1. And preparations must get under way soon for the next budget request, which Reagan will submit to Congress in January.

In a speech delivered April 21 to the Association of Private Enterprise Education, Miller indicated that his approach to the deficit may be somewhat different than Stockman's.

Calling for a return to economic "fundamentals," Miller said that "much of the current hand-wringing over the federal deficit" is a reflection of "old government-centered thinking" that was "repudiated at the polls" in 1980 and 1984.

The chief question about the deficit, he said, should be its impact on the economy, and he suggested that big increases in business investment over the last two years "suggests there is no need for panicking responses to the deficit."

Miller said the deficit has "some real costs," such as larger interest payments on the national debt, which increase the "burdens to be shouldered by taxpayers in the future."

"But I submit the deficit is a symptom of other problems, not a disorder to be treated in isolation," he said. This is the reason, he added, that people "have refused to be stampeded into support for higher taxes . . . ."

"Obviously, the deficit can be 'explained' as a matter of inadequate tax revenues. But real economics reminds us that the challenge is not simply to enhance government revenues, but to do so in a manner that does not interfere with growth . . . .

"A growing economy will produce growing revenue for the government," he said, "while tax increases that hinder growth may ultimately prove counterproductive for the Treasury as well as disastrous for the public in general."