The bullet inside the chest proved -- amazingly -- not all that serious and as the president recovers, the national thanksgiving rises to 100 percent that this near-tragedy has turned out so well.

The Reagan White House, in any case, has been reported in a euphoric high ever since the election and even so cautious a reporter as Elizabeth Drew has detected signs on Pennsylvania Avenue that the Reagan team is enchanted with its general success in "winning Washington."

It's important to any president to have the capital soundly behind him and to start with a great geyser of good will since, no matter who a president is, the people whose interests are necessarily gored (they vary, but the gored we have always with us) are not going to be pleased with him by the time his administration ends.

With delicacy and tact, therefore, I suggest that while everybody agrees the president is warm, outgoing, likable (courteous, loyal, kind, brave, reverent, zub) the winning of Washington is not quite in the bag.

One of the first public signs that the president has a way to go yet may be seen in the reaction of youngsters at Alice Deal Junior High School here. Those are not tots at that school, but if my arithmetic still serves, are teenagers.

A teacher there wisely opened a discussion on the attempted assassination and, allowing for a few raging hormones that commonly hamper the young in matters of balance and judgment, the overwhelming view was of course that such attempts are unspeakably evil, and there would be no point even thinking of Alice Deal if this obvious verdict were all that surfaced.

But in the discussion at the school it turned out that surprising attention was given to the president's reception at the emergency room of George Washington Hospital. The question kept surfacing, why were other patients at the emergency room told to "get the hell out" by the Secret Service?

The retort, I guess, could be simply this:

"Would you prefer the president to stand in line with blood coming out his mouth, until Jenny Smith got her tetanus shot?"

It's not quite that simple, though. The mere fact that the young people seized on the preferential treatment of the president suggest to me, at least, a major failure of the president in his campaign to win Washington.

The chief political task of the president, no matter what they say, is to persuade his subjects that his economic policies will work (certainly the liberals have failed) even if the general idea is to liberate the rich so that, in due time, some gold and liquid joys will sift down to the poor. And since the vast majority of Americans are suffering from inflation that has not been cured by any of the standard remedies, most Americans gave Reagan a mandate to try his own snake oil.

The trick, clearly, is to keep everybody in a good humor until eventually maybe some improvement is detected, buckwise. You may further guess that as budgets are cut severely for services used mainly by th poor, that it is specially important to keep the poor (less than $63,700 a year?) from becoming restless.

If you are going to cut services, maybe you should be as appealing, personally, to those who suspect they are going to bear the brunt of the experimenting, as you possibly can be.

The president and his wife began the general courtship of the poor, or at least began this administration, with a great flurry of white gloves, and rich friends who tended to think the bums sleeping on the heating grates by the State Department really should be swept up, you know, since they really are not very ornamental.

The president can hardly be blamed if people prefer to get the price of Nancy's pocketbook straight in their minds rather than the president's economic package, and the White House may have some grounds for complaint that a frivolous press pays undue attention to the number of inaugural limousines and the cost of presidential trips to California.

As I recently demanded of my wife -- who last had a kind word to say for Adlai Stevenson and nobody since -- would it be better if the president got an excursion-rate bus ticket, with layover privileges to catch up on sleep in Amarillo?

We have not heard a great deal of Nancy Reagan's conversation, recently, and I wonder if someone has suggested her remarks are so likely to be taken out of context that perhaps she should say little.

It is possible that any image conveyed by (or manufactured for, or foisted on) a president is false. It is possible that many people may advance themselves by unfairly sniping at the frivolous edges of a serious political leader.

The prevailing view is that he is winning Washington and adding daily to the number of citizens who trust him.

The prevailing view is, unfortuantely, wrong. The president is being perceived as a man who has too much faith in the rich and not enough in the poor. Too many Sinatras and Annenbergs, too many special privileges, too great a bursting forth of arrogance based on wealth.

What a president hears, what his polls tell him, what his sycophants and fawners tell him, usually has nothing much to do with reality.

President Kennedy was assured up one side and down the other by his own particular range of imbeciles that the Bay of Pigs was just the thing. It was otherwise, and if he had himself lived, it seems to me certain he could not have won re-election after that misjudgment.

President Johnson, who had God's own plenty of flatters, was praised every day and twice a day for his manly stance in Vietnam, but at the last he began to understand he could not be elected dog catcher of Anacostia, and you rather wonder what ever happened to his total public support in his Vietnam adventuring, or to all those advisers who cheered him on down the road to political ruin.

Presidents rarely have the luxury of doctors, to bury their mistakes, and since we know to begin with that presidents are not quite a dream-mixture of Einstein and St. John of the Cross, it is unfair, maybe, to reproach them for not being blue-chip saviors when they are merely politicians doing the best they can.

So the incumbent president would do well to take with a grain of tarragon (surely they do not use anything as common as salt at the White House now?) the general assurances that he hears from all sides that he is on the way of being more loved and trusted than Walter Cronkite, Mickey Mouse, Marilyn Monroe, Ma Bell and Abraham Lincoln all put together.

The young people unnaturally concerned about special privilege at the emergency room -- though I have already given a reasonable and standard answer to their complaint -- are a shadow no bigger than a kid's portfolio of Treasury notes. All the same, when I read their reaction, a million little coordinates clicked together in my admittedly sorry brain, and I knew this was a more important thing than the somewhat surface babble of analysis going on on television at the moment.

If the president's "stage managers" are as clever as we keep hearing they are, then one of the president's first acts will be a visit to Alice Deal; Junior High or, if that is a bit too obvious a step, some other symbolic move to associate himself with nonsinatrid America.

They say that when you look death in the face, as the president has just done, one reward of the terrible experience is that values somehow sort themselves out in a wonderful way. It may be true and I hope so.