The White House is mounting what one senior administration official calls "a full-court press" in an effort to reverse a growing public perception that the United States is spending too much money for military purposes.

In an unannounced campaign to counter a trend in public opinion that has emboldened congressional critics of President Reagan's defense budget, prominent administration officials who rarely speak on military matters have been instructed to defend the U.S. buildup at every opportunity.

William Greener, a Pentagon and White House spokesman in the Ford administration, has been brought in as a consultant to coordinate speeches and public statements. And White House officials say that, within the next few weeks, Reagan will make another nationally televised appeal for his defense budget, probably tied to a key vote in Congress.

"He needs to go on television, he needs to build support in Congress," a key Reagan political operative said. "The case is still there to be made, but the paradox is you've got to make it in such a way that it does not awaken the nuclear freeze impulse."

Reagan has been complaining, publicly and privately, that support for his defense policies has eroded in the face of a "drumfire" of media criticisms.

Last week, the president told a group of editorial writers in the White House: " . . . I think this steady drumbeat and this criticism from up on the Hill has created a false belief among too many people in this country that, maybe, in one or two years, we've solved the problem, but we've got a long way to go before we really can say that we are able to meet the first prime responsibility of the national government, which is to be able to guarantee the safety and security of the nation and our people."

White House communications director David R. Gergen said the turning point in administration perception began with a Louis Harris survey in Business Week magazine last November that showed a two-year decline, from 71 to 17 percent, in the number of Americans who thought that the United States needed to spend more on military defense.

Gergen said other surveys, including those by Richard B. Wirthlin for the White House, have since reported similar findings.

In January, a Washington Post-ABC News poll showed that 59 percent of Americans were willing to cut the defense budget to reduce the federal deficit, up from 41 percent a year ago.

These findings coincided with the concern of national security officials that Secretary of Defense Caspar W. Weinberger was being left out on a limb while some White House officials undermined the president by failing to campaign ardently for the defense buildup.

White House chief of staff James A. Baker III was especially suspected of taking a less-than-enthusiastic approach to the defense budget, since he had made it known on Capitol Hill that he agreed with some Republican senators that the budget could be reduced safely.

Other targets of the complaints from national security officials were two Baker allies, presidential assistant Richard G. Darman and Office of Management and Budget Director David A. Stockman.

Over the objections of national security adviser William P. Clark, Baker prevailed in his recommendation last fall that Reagan stay out of the campaigns on nuclear freeze initiatives, approved by voters in eight of nine states and the District of Columbia. But even officials who agree that this decision was politically wise said White House officials have spoken out insufficiently on behalf of the defense buildup since the election.

"There has been a perception that there's only two people in the Reagan administration speaking out for defense--the president and Cap Weinberger," one official said recently.

The sensitivity of the defense-minded members of the administration was heightened by the noticeable efforts of Baker and Stockman to persuade Reagan to make reductions in his proposed defense budget, including a one-year freeze in military pay.

On the other hand, some officials close to Baker have complained that the Defense Department has not given them much of a case to take to the public.

"We asked for talking points and they brought over books," one White House official said. "It was difficult to understand what they wanted us to do."

This conflict came to a head in the final days of budget preparation late last month, sources said, spurred partly by Reagan's irritation at stories that he was being manipulated by his staff to reduce projected defense spending increases and to make other budget concessions.

At a high-level White House meeting, it reportedly was decided that top-ranking staff members and Cabinet officials would try to make a frequent, and unified, case for the defense budget. A principal "talking point" is one that Reagan used often in the 1980 campaign: that U.S. military spending must be determined not by the nation's budgetary needs but by the persistent and continuing Soviet arms buildup.

"We have all agreed that Cap needs help and that it's the responsibility of everybody in this administration to rally around on this issue," Gergen said.

For this purpose, Greener, who has shown the ability to present complex defense issues in plain language, has been brought in to coordinate speeches, news releases and "talking points" dealing with the defense budget.

The result has been a new, coordinated emphasis on defense in recent statements by administration officials. Last week on "Face the Nation" (CBS, WDVM), Stockman made an unusually strong case for the defense budget in words similar to those often used by Weinberger.

White House counselor Edwin Meese III emphasized the defense issue in a subsequent interview. Even Baker, who usually focuses on economic and political issues, has begun to speak out strongly on behalf of the defense buildup.

It remains to be seen whether this "full-court press" will be successful. The administration's political problems with the issue stem in part from the fact that Reagan has kept his promise to increase the military budget but has failed to produce the economic recovery that was also a cornerstone of his campaign.

"We're perceived as not having succeeded, at least yet, on the economy," one official said, "while there is a widespread perception that the president has kept his promise to increase the defense budget. People are now saying that enough is enough."

To counter the impression that the administration is lavishing budget resources on defense while starving domestic social programs, Reagan and members of his administration have begun to point out that the defense budget is only slightly higher than what Jimmy Carter had projected for the same year.

Carter's January, 1980, budget projected defense spending outlays for fiscal 1984 of $232.3 billion. The budget Reagan recently sent to Congress called for defense outlays of $238.6 billion.

Coincidentally, this belated credit that Reagan is giving to his predecessor undercuts another favored presidential argument: that the Reagan administration has begun to reverse a long U.S. military decline.

Reagan has frequently, and accurately, observed that the trend toward spending a lower percentage of the gross national product on defense began during the Kennedy administration.

Usually, he has failed to add that a reversal of this trend began under President Ford and continued under Carter.

Now, however, Reagan is more than willing to share credit with his two immediate predecessors as he seeks to recreate a bipartisan coalition for his defense budget.

"President Kennedy once said there was no discount on defense," Reagan told a group of out-of-town editors and broadcasters last week. "He was right. And I think the American people knew that he was right.

"The defense issue is one of the most potent in American politics, and time after time the American people, when given the facts, have made it clear that they support a strong defense program," Reagan said. "They've never had patience with politicians who want to have a fire sale on national security or a bargain-basement military, but right now they've had a drumbeat of criticism based on false charges.

"Defense spending is not the cause of our economic problems, and without it we'd have no chance of negotiation on arms reductions and getting an agreement with the Soviet Union in that field."