A confident David A. Stockman said yesterday that the administration, with the help of the American public, will win passage of President Reagan's tax plan before Congress recesses in August.

In an appearance on "Issues and Answers" (ABC, WJLA) Stockman, director of the president's Office of Management and Budget, ruled out any further compromise on the tax plan and vowed that the administration "will move into high gear in terms of calling the attention of the American public to the tax bill." Action before recess is vital if the changes are to be made in time to "give people the tax relief they need" by 1982, he said.

Meahwhile, Treasury Secretary Donald T. Regan yesterday predicted that the economy will decline in output in this quarter and said it is "possible" interest rates might begin to decline this week. Earlier reports of the Reagan administration's economic forecast, to be issued this week, said it would predict a stagnant economy but would stop short of forecasting any periods of negative growth.

While Stockman said he expects a fight over the tax bill, he was sanguine about the upcoming congressional conference on the other half of the president's economic package -- the budget bill. The OMB director referred to what he called an agreement with the House leadership that no substantial changes would be made, and said the leadership had agreed to complete work on the conference by July and to appoint no conferees who had voted against the bill.

House Budget Committee Chairman James R. Jones (D-Okla.), however, has a slightly different recollection of that agreement. Jones said yesterday that the House leadership had agreed to work expeditiously but to no certain deadline, and that it had agreed only that a majority -- not all -- of the conferees would be members who had voted for the budget bill.

The biggest differences between the administration and House Democrats on the tax-cut package is over the magnitude of cuts in individual taxes. The administration is holding out for a 25 percent cut over 33 months, while House Democrats are moving toward a smaller cut over 24 months with relief tilted more toward middle- and low-income families.

"We belive and the president belives that that we have compromised enough already," Stockman said, noting the administration had moved from a 30 percent tax cut proposal. Last week the White House rebuffed Republican congressional leaders who wanted to keep open the possiblility of compromise.

"The American people in overwhelming proportions support the president's economic program," Stockman said. The notion that there is more support for budget cuts than tax cuts is a misreading perpetuated by the media, he said. He also said there was room to make more cuts next year.

Stockman dismissed reports that defense spending is likely to run as much as $10 billion over projections for the next fiscal year, which would threaten the Reagan economic program. "I don't think we'll need more money," Stockman said, although he did not rule out that possibility. Predictions of overruns were caused by bureaucrats leaking wish-lists, he said.

Stockman also defended using more conservative projections about Social Security deficits than on other issues such as the budget, citing the "solemn national obligation" to make sure the fund is sound.

Regan, is an appearance on "Face the Nation" (CBS, WDVM), challenged Democratic tax proposals as "redistribution of wealth rather than a bill creating wealth as ours is" and said that only the president's tax plan would stimulate the economy.

Democrats, he said, are "trying to buy their way to victory over us" and have actually included tax breaks for wealthy commodity traders and oil companies in their proposal. House Speaker Thomas P. (Tip) O'Neill (d-Mass.) and House Was and Means Chairman Dan Rostenkowski (D-Ill.) said that Regan's characterization was inaccurate.

Regan also said the administration is revising its predictions for this year's deficit back up to $55 billion because of higher interest rates the federal govenment has had to pay. Less than two weeks ago the administration had lowered the deficit projection to $51 billion or $52 billion.

The treasury secretary said is not happy with high interest rates but that they are "like bitter medicine -- one of the side effects of our fight against inflation."

"As inflation gets down and stays down, rates will come down," he said.

U.S. allies are not happy with high interest rates here but they understand the need, Regan said. "We know it's a temporary phenomenon. It's in their long-term interest to see that American gets its inflation rate down."