AT THE WHITE HOUSE and in congressional committees investigating the shooting of President Reagan, a great debate is going on about what, if anything, can be done to better protect the president of the United States.

Many of the parties involved in this discussion have a favorite scapegoat or whipping boy. Everyone agrees that Secret Service agents Timothy J. McCarthy and Jerry Parr performed heroically and probably saved Reagan's life, but there are those who think that the Secret Service could perform a better job of crowd control or of keeping crowds away from the president.

There are those who blame the press for supposedly making the president more vulnerable than he otherwise would be. There are those who blame the White House staff for putting politics above protection. And there are those who blame the FBI for not telling the Secret Service all it knew about the suspect.

Okay, so we have a need for scapegoats, and all of the above are understandable reactions to an assassination attempt which came as near to success as this one. They are understandable reactions, but they are also wrong. Before we devise new procedures to insulate the president from the press and the public because of the horror of the shootings at the Washington Hilton, it is worth looking at what will be lost in the process.

There are times when a president needs to get out of the White House, as this president and his wife like to do on Sunday mornings when they stroll to church. There are times when a president holds so few press conferences (of which more later) that it is necessary for a wire-service reporter to buttonhole him with a timely question.And there are times when a president, or a presidential staff, finds it irresistable to "work the fence" and shake the hands of those whose support he is seeking in the next election.

All of these features of the American political system can be dispensed with, of course. If they are, the president will have become a prisoner in the White House. In a very real sense, the mindless assassins will have won.

These are not the views only of those who cover the president.They are the opinions of Edward J. Hickey, the man who has protected Reagan for most of his political life. Hickey, whom Reagan used to call "Boston Blackie" because of his resemblance to a movie character of that name, worked for six years in the Secret Service and another six providing protection for foreign dignitaries in the State Department. For seven years in between he was in charge of Reagan's security in California. He is now Reagan's military aide and the point of contact for the Secret Service within the White House.

"If the president becomes a prisoner, you've changed our free society," Hickey says.

It is Hickey's view, which I share, that the Secret Service demonstrated its professionalism in the Reagan shooting, reacting the way agents are supposed to do in the textbooks. Hickey believes that it may be desirable in some circumstance to keep crowds further away from the president but that each instance has to be evaluated on a case-by-case basis and that it simply is not possible to decree that the president has to stay away from crowds as a matter of course.

What is possible, he thinks, is to avoid preannounced minglings with crowds, which give assassins the notice they need. The White House, with the cooperation of major news organizations including The Washington Post, took a step in the direction of removing this notice last week by announcing that in the future the times of the president's and vice president's public appearances would be given only on a background basis instead of for publication. This was amended later to apply only to Vice President Bush, but it is widely assumed that this will apply to Reagan, too, once he starts going around in public again.

No one is giving up anything precious in this common-sense procedure. But it would be something else again if reporters relinquished their long-standing practice of asking questions on the run.

An illustration of the usefulness of such questions came last July 4 at a town meeting in Merced, Calif., when President Carter answered a question about the status of hostage negotiations by saying he had just been in touch with the State Department "and with others that I can't name publicaly in trying to have an avenue to the Iranian leaders to get our hostages released." Reporters didn't know whether this was simply a political answer or actually presaged some significant development in the hostage situation. They would have been left to write a confusing story except that Helen Thomas of United Press International, the senior White House wire service correspondent, buttonholed the president just before he climbed aboard a helicopter and asked him what was up.

"We're trying different things -- nothing special," Carter replied. "I can't predict any breakthrough. We're just all the time trying different things."

The answer told reporters what they needed to know, which was that Carter's answer had been a political comment, not a hint that American hostages were about to be released.

The two U.S. wire services are always present in the reporting pool which travels with the president, and it is the wire-service reporters, with their focus on breaking news, who ask many of the running-comment sort of questions. Often the questions and the answers to them are unproductive or insignificant, but sometimes they are the only link for months at a time between the president and the people of the nation. As a White House correspondent in the final months of the Nixon administration, I know how isolated and insulated a president can be. And even Carter, who ranks as one of the most accessible of modern presidents, proved something else again during the 1980 campaign after his hostage strategy backfired.

It is not necessary to ask these questions on the street. They could easily be asked in the total security of the White House, at the various daily "photo opportunities." Or the president could agree beforehand to stop before the reporting pool in the security of the hotel or hall where he is speaking rather than on the sidewalk. The reason these stops aren't made, more often than not, is not a security one but because the staff doesn't want its leader to make ad hoc remarks which might detract from his prepared message.

Ronald Reagan as president has steered a middle course between the poles of openness and inaccessibility.. In his first 70 days he held two press conferences, granted interviews to the networks, The Washington Post and the Harvard Crimson, attended an editorial board meeting of the New York Daily News and met with columnists in his office. But Reagan's track record suggests that he, too, will be accessible or inaccessible as the political situation dictates. In 1980, Reagan started out with a closed-circuit approach, became highly accessible after his defeat in; the Iowa caucuses and remained so until his managers secluded him for a few days after a series of gaffes in late August and early September. He then became accessible again.

On the campaign trail or at speeches outside the White House, the press pool often acts as a buffer for the president, or as what Thomas calls "a human shield." The Secret Service has on occasions welcomed the ringing of the president with cameramen. As Susan King of ABC observes, the pool was used to shield President Reagan when he abruptly decided to depart from a secured area to greet nurses and staff the day he went to Walter Reed Hospital to visit Sen. Bob Dole.

"There are many occasions when a president is less vulnerable rather than more vulnerable because of the press," says King.

That is true enough. But it is also true that with or without the press, and even with the best protection in the world, presidents will continue to be vulnerable in a free society. They will not be noticeably safer if reporters, none of whom has ever been involved in an assassination attempt, are kept away in the name of protection while presidents are freely unleashed in the campaign system to approach any crowd of their choice.

It would be safer for presidents and candidates to restrain these impulses. It would be safer for them to go directly to their cars without pausing to answer questions. And it would be both safer and more useful in terms of public communication if there could be an understanding that presidents would agree to stop regularly in secured areas to answer questions. When such stops are scheduled in advance, they can be built into Secret Service schedules so that the timetables dearly loved by protective services are not violated.

This approach won't do much to satisfy those who would prefer to find a scapegoat for the shootings at the Hilton. But if adopted by the Reagan White House it would be a demonstration that the administration understands the vital difference between the protecting a president and isolating him from the press which covers his daily activities.