PRESIDENT REAGAN'S extraordinary skills in using television quickly led to his being dubbed "The Great Communicator." But a careful look at his performance so far reveals another characterization that may prove far more lasting -- Reagan as "The Great Legitimizer."

The president is bringing to the surface and "legitimizing" a new political agenda -- an agenda that would, if adopted, signal the country's ultimate rejection of the president's own deeply held views.

Why is this happening? Because Reagan has chosen to govern by ideology. He rejects the traditional presidential path of seeking national consensus in order to command the great middle of American politics. Instead, Reagan remains committed to implementing an ideology that lies substantially to the right of most citizens. He edges toward the middle grudgingly, only when forced.

A president cannot ultimately set and dominate the national debate in this country from the far right or far left. By giving up the center, Ronald Reagan is leaving the political arena wide open for those who reject his vision of America to reach out to and rouse the country's always hard-to-rouse middle.

As a result, new political movements are surfacing and gaining momentum. They are providing new ways to look at old issues. And they are increasingly diminishing this administration's ability to set the agenda for the 1980s. Take just four examples.

1. Nuclear arms policy. After decades of leaving it to the experts, the country is at last engaged in debate over the paramount issue of out times -- nuclear arms and the risk of nuclear war. An extraordinary grass roots movement aimed at ending the nuclear arms race is sweeping the country. The nuclear freeze movement, Physicians for Social Responsibility, Ground Zero and others have played a vital role in attracting millions of previously uninvolved citizens to this battle.

But can anyone doubt that Reagan himself is the father of this movement, the principal force in unleashing the outpouring of concern? Where, after all, was this national outcry for arms control in 1979, when the SALT II treaty was before the U.S. Senate?

The president's early hard-line policies and harsh rhetoric have triggered a nationwide nuclear arms control movement that is going to be with us for many years to come.

2. Fairness. The 1970s were a period of growing resentment by the middle class toward those at the bottom of the income scale. With inflation squeezing everyone, many Americans came to believe that government programs were unfairly tilting towards the poor at their direct expense.

Reagan's policies have dramatically changed this political dynamic. His budget cuts have focused most on curtailing benefits to the poor. His tax cuts have focused most on providing benefits to the wealthy. His 1981 tax bill has turned out, in fact, to be the greatest government-sponsored income redistribution program in history -- though not in the traditional sense of the concept.

You don't find too many people today accusing the Reagan administration of unfairly tiliting towards the poor. Instead we are seeing the emergence of a shared concern between the middle class and the poor over government policies that unfairly tilt towards the wealthy. And it is this fairness question that is going to be a central issue in the 1982 national elections and the Congress that follows.

The issue already has led the GOP-controlled Senate, belatedly backed by the president, to pass a tax reform bill that closes a number of corporate and individual loopholes -- a bill liberal Democrats would have been proud to call their own a few short years ago. It has also set the stage for a new national debate about fundamentally restructuring the tax system. And it has raised a whole series of concerns about how the burdens of sacrifice can be more equitably distributed during periods

3. Military Spending. President Reagan's rigid insistence on enormous increases in military spending during difficult budgetary times has been successfully carried out so far. But it's been done at a very heavy cost: The president has managed to shred the security blanket that "national security" has always provided for military spending.

As a result, in 1982 candidates of all political persuasion will raise serious questions about the size of our military budget and whether those funds are being spend wisely and effectively. They will do so free of instant vulnerability to the charge that they are anti-defense or naive about national security.

With Republicans and Democrats, conservatives and liberals, openly challenging the administration's military budget as excessive, a basic change is occurring in the politics of military spending. It is losing its immunity.

The powerful coalition that has long dominated this issue still holds the high ground. But it appears headed for its first serious challenge, and perhaps for the fight of its life, in the years immediately ahead.

4. Government. The Vietnam war, Watergate and a steadily worsening economy all served as major factors in making the past two decades a period of intense citizen disillusionment with government.

This disillusionment culminated in Reagan's 1980 candidacy, which attacked government head on. His victory brought to center stage what is likely to be the core domestic debate of the 1980s: how to reshape and redefine the role of government in our lives.

But as this epic debate has started to unfold, a remarkable development is taking place. We are seeing brought back into national perspective the fact that government plays a positive role in our society -- as well as a negative one -- by a man who does not believe this to be the case.

Ronald Reagan came to the White House with the basic view that government is inherently evil. He continues to hold this view. He argues that the private sector holds the answer to all our problems, and seeks to eliminate basic government services.

But most citizens do not want to abolish government. They want a leaner, more efficient, more effective government.

Reagan's absolute anti-government views ar reeducate Americans about the legitimate benefits of government. But, more importantly, they are serving to count him out as a leader in the effort to shape a government that suits the needs of the 1980s and the decades to come. The 1980 election, in short, was a mandate for problem-solving change in America. It was not a mandate for rigid ideology. Reagan's refusal or inability to recognize this, as much as anything else, is rousing the broad center against him and creating historic opportunities for others to redefine the national agenda.

As a result, it's starting to look like the Reagan presidency may well be best remembered not for the ideas it espoused, but for the ones it legitimized.