Until he sent Americans to die ignominiously in the desert, President Carter had been performing one of the greatest actss of political levitation in our history. Despite conditions at home and abroad that would have spelled political doom for most of his predecessors, he continued to float serenely above the fray. Blow after blow had befallen his presidency, yet he remained relatively unscathed.

Carter's success hasn't been mysterious; he has stayed aloft through the sufferance of the people. When all else has gone wrong, they have sustained him. Now, Carter has had his Bay of Pigs, a truly historic disaster, and that extraordinarily complex, strong but fragile bond between Jimmy and the people will be put to its severest test.

After the Bay of Pigs invasion of Cuba in 1961, John Kennedy was bemused. He had just completed his first 100 days in office, that arbitrary number that supposedly marks the end of the presidential honey-moon with public and press.

If he had been a British prime minister, he said, he would have been thrown out of office after such a defeat, yet the political reaction at home seemed only to have enhanced his prestige.

At that point, Kennedy's personal secretary, Evelyn Lincoln, entered the presidential office carrying an advance copy of the Gallup Poll, the latest since the American humiliation on the Cuban beaches. Despite his failure, Kennedy's popularity had risen sharply: An unprecedented 82 percent of the public then backed his handling of his job.

It's just like Eisenhower," the young president said, "The worse I do, the more popular I get."

It is unlikely that Carter will be accorded such support after the tragic adventure in the Iranian desert. He's been slipping again, and you get the sense after talking with voters that he's in danger of being over-whelmed by all the bad news. Certainly the forces necessary to topple a Democratic president exist -- unprecedented inflation, rising unemployment, further deteriorating economic and international situations, and growing fear of the future.

What's remarkable is that until now Carter has survived in the face of all these problems. He has managed to do so because of one basic belief -- that Carter, whatever his faults, is doing his absolute best for the public.

People chose Carter because of his personal qualities -- because he was like them -- after all the heartbreak and disillusionment with public leaders over the past generation.

They have clung to the hope that, in the end, he won't let them down.

Better another imperfect president, people seem to feel, than another fallen angel.

That's where things stood when the illfated mission into the desert was lauched.

Some personal examples: in the days immediately before the rescue operation I conducted lengthy interviews with voters in a wide area ground Akron, Ohio. The experience strengthened the feeling of paradox about Carter. While Carter obviously was being criticized far more strongly than in previous months for failing to take effective action on the economy and on Iran, it was clear that he still received a layer of sympathy.

Carter doesn't have the feisty Harry Truman give-'em-hell and come-from-behind syndrome going for him. Nor is it a feeling of pity that helps him with the public. It is the politics of sympathy that has been working for him.

To many people, Carter has been viewed as an Everyman in the White House. He's the little guy struggling with the big problems. However harshly they judge his performance, they have granted him respect. And something more: They have been identifying with him.

"I didn't vote for him," a suburban housewife north of Akron said, "but as a person I feel empathetic toward him. I feel he's trying. He is sincere. He hasn't done what the people hoped.

"If I were too know him on a personal basis, I think I'd find a nice person who really wants to do a good job. He's just an average guy, maybe in over his head. But I don't think a president can solve everything. Presidents are not supposed to be king or emperor. I wonder how that man gets any sleep and puts all these things aside. It must be a terrible strain. What an awful job! I feel sorry for him sometimes."

More than sympathy has been at work for Carter. The public yearning for leadership continues, buttressed by another desire -- for stability and continuity in the presidency after so many years of turmoil. Thus, you'll hear people say, "It takes more than four years to solve the problems," or "He didn't create them." They have wanted him to succeed. Not for himself but for them. And they also have been reluctant to admit they made a mistake about Carter.

That doesn't mean they are certain to stay with Carter in the fall as they have so far in the spring. Nor that they think Carter, however sincere, decent and moral they believe him to be, the perfect president for the times.Even before the failure in the desert, evidence strongly was pointing otherwise. Clearly, many people have been reassessing the qualities they think they want in a president. The results are interesting.

Kathy Foster of Hudson, Ohio, for instance. She couldn't stand Nixon, she said, but looking back she found virtues in him she didn't then appreciate. At least he could make decisions, she said. Then:

"I don't know if I prfer someone with a seamy side like Nixon who was politically astute, or someone like Carter who is a good moral man but not politically astute. I'm really torn. If we could find one with both qualities -- politically astute and moraly sound -- boy, would we have it made."

For people like her the tangle over a president like Carter now becomes even more complicated. He has just demonstrated he can make tough decisions, but can he make the right ones?