In the jargon of the White House press operation, it was what is known as a "photo opportunity." It was one in a series designed to counter the growing perception that President Reagan doesn't care about the struggles of ordinary folks in the worst economic slump since the Great Depression.

As Reagan and his presidential party drove from church in the depressed coal-and-lumbering hills of eastern Tennessee last Sunday, the entourage suddenly stopped, after traveling just 200 yards, in front of a tumble-down, gray-shingled house with a green stone frog and two gilded lions out front.

Into the midday sun and out from behind the thick wall of security emerged Reagan and the First Lady and their host for the weekend, Senate Majority Leader Howard Baker. The stop caught the traveling press corps by surprise, to say nothing of the effect it had on 71-year-old Princess Caldwell, a logger's widow and retired cleaning woman, up whose front steps the president of the United States climbed.

As Reagan and his party shook hands and exchanged pleasantries with Mrs. Caldwell, her 88-year-old mother and 61-year-old brother, the cameras recorded the scene. Shortly, Reagan retreated back into the presidential limousine, fielding a few question about the battle in the South Atlantic before the entourge sped off. The entire event did not take up a full 10 minutes. Abruptly as it had begun, the "photo opportunity" ended.

There is no record of what was said on the elderly family's front porch. Presidential advisers recall only scraps of banter about children spinning tops and shooting marbles nearby down on the old courthouse square in their little village of Huntsville (pop. 519 in 1980), or about the hard times the barking dogs in the backyard had given the Secret Service when they conducted a sweep of the premises. A stunned Mrs. Caldwell, overcome with excitement, could not remember the exchange either.

"I couldn't tell you exactly what he said to save my life," she remarked later with mild embarrassment. "He talked real nice."

She and her mother and brother do remember that, out of a sense that it would somehow be inappropriate, they did not bring up -- and the president did not ask -- about concerns they would raise later with some degree of anxiety in telephone conversations with a reporter. Which is a pity and the reason last Sunday's "photo opportunity" was for them, and for the president, a missed opportunity.

Caldwell, a breezy, chatty woman, still giddy about her brief encounter with the president, speaks with an air of brave desperation about an up-and-down life that has left her suffering from diabetes and frequent dizzy spells and trying to make ends meet on an income of food stamps and federal old-age benefits.

She believes in the president, voted for him, but will not believe that his cure for the economy has slowed inflation and stabilized prices. "Not here, they haven't," she insisted. "These big supermarkets, the prices are out of sight."

Her heating bill shot up to $100 in the cold months of the winter, electricity runs about $50 a month, and then there is the $55- a-month premium for the insurance on the house, a payment she sometimes lets fall behind. "You can just imagine how much I have left. I don't complain," she said.

Medicaid covers most of her health costs, but the doctor told her to take vitamins, which she must pay for herself, and she tells you that she pays $7 for a big bottle of vitamins and that it contains exactly 90 pills, enough to last her and her mother 45 days.

And as is often the case with the poor, there has been the disruption of unforseen personal catastrophe, like the time she was behind on her home insurance and fire erupted on the second floor. That was three years ago, but it was only the day before Reagan's visit that she had paid a man to come out from Knoxville to replace six windows destroyed in the fire.

She said she went into savings and shelled out the $90. Figuring that he might glance over at her house when he went to church across the street, she said she did not want Reagan to think that "bums, trash," lived there. On that Saturday, she had also gotten up and cut the grass out front, mowing for a while, then lying down again during the frequent times she was overcome by "weak spells."

"I don't get by too good, but I get by," she said. "I'm the type that don't give up."

She said she liked Reagan when she met him, found him to be friendly and personable. She had voted for him in 1980, not knowing a great deal about him, making the choice because it had been the public recommendation of the favorite son of east Tennessee, Howard Baker, a man for whose family she had once cooked and cleaned and in whom her faith and trust are total.

Princess Caldwell pleads ignorance about most national issues, begging off declaring views. But when she talks about benefits and the talk of cuts coming down from Washington, there is a tone of quiet desperation. Her conversation then is punctuated by quick, sharp bursts of nervous laughter.

"I hear some of them talking that he's talking about cutting the checks down," she said, protesting that if the cuts are made, the people getting the big checks ought to be the first to sacrifice.

"Now if he cuts the little fellow like me and mom, I don't know what we'll do." Long, deep breath, followed by another burst of the sharp laughter.

"It takes all we get just about to pay for what we eat and pay our bills, water bills, sewer bills, telephone." Pause, followed by ironic laughter that is chilling.

At one point, she says simply and matter- of-factly, "I hope they don't cut mine. If they do, they'll ruin me."

In March, at last reading, the unemployment rate in Scott County, Tenn., went over 17 percent. The slots in the CETA-training program -- in which her 61-year-old brother Finley Farmer is enrolled -- are coveted. Farmer was out of work for months after leaving a job with the Indiana highway department, complaining of breathing problems -- "asthma or something," he said.

Though local officials said that stipends paid to CETA workers had to be reduced because of last year's budget cuts, Farmer and his sister are pretty happy about the $100 a week he gets for 40 hours of training in how to operate heavy equipment.

"A fellow like that can live on that," Caldwell said brightly. Now he buys his own food and cooks his own meals, helps care for their mother and, she added, "that makes it nice."

The training program is to be completed in August, but Farmer is not certain he will find work. But there are many in the hills who would trade places with him right now.

It might have been useful if the president had talked to them about these things, rather than have his picture taken.