IN FRANKLIN D. Roosevelt's early years as President, his small grandchildren Buzzie and Sistie Dall lived on the third floor of the White House. Sometimes they could hear the band playing downstairs. They would have sedate birthday parties with ice cream and cake and creamed chicken and guests they didn't always know very well.

The press would report the parties afterward from hearsay.

Once in 1834 a reporter broke through the security when the Dall children were vacationing on Plum Island in Wisconsin and got an interview with 7-year-old Sistie. She liked to swim, she said. This information was copyrighted by a wire service and sent around the world.

The same year, in another copyrighted exclusive, she was quoted by "her faithful colored nurse" as wanting to be called by her right name, Eleanor. "They weren't names that other folks were to call us . . ."

To this day, whenever Mrs. Van H. Seagraves, now 50, turns up in the news, she is referred to as Sistie.

The President's family has always been more or less public property. But since television, and especially since the cult of celebrity flowered in this country, life for anyone residing in the White House has become grotesque.

"There's no way to satisfy the insatiable appetite of a growing industry like the press," commented Elizabeth Carpenter, a Washington hand for 34 years and for six years press secretary to Lady Bird Johnson. "The press doesn't like to be called an industry, but it is, and that has to be said twice a day."

When Lynda Bird Johnson was married to Capt. Charles Robb in 1967, the first White House wedding of a President's daughter in 53 years, the press went out of its mind. Someone had to know how many raisins were in the wedding cake. Did she dye her hair? And "from the minute she walked down the aisle," as Carpenter put it, "people were asking if she was pregnant yet."

The year before, at the wedding of her younger sister, Luci, there was a terrific to-do over the bride wearing Cuban heels.

There was also the flap over Luci's hamsters. Carpenter had the good, gray Associated Press hanging on her door to ask what the gestation period of a hamster was.

"That's not why I went to journalism school," she said in a recent phone interview from Texas.

Sometimes it was wose then silly.

Lynda and Luci Johnson would go to sleep hearing the antiwar marchers outside chanting ugly things about their father all through the night.

Margaret Truman's debut as a singer created an uproar all out of proportion, though as she now says, "That had its advantages as well as its disadvantages."

Julie Nixon Eisenhower, who left the White House two administrations ago, still has to listen to public accusations that she acts "too restrained" or has some other personality defect. When she and her husband, David, go looking for a house in Bucks County, not only is the fact reported, but readers are treated to the unsolicited remark that the "poor dears are confined to the $150,000 range."

Of course, White House families have always been news. Even their pets have been of such avid interest that Margaret Truman wrote a book about them. When Alice Roosevelt, Theodore's daughter, smoked in public there was a terrific outcry. But that was perhaps a sign of the times.

Today, with more than 1,600 people holding White House press credentials, nothing is too trivial for the press and the pop culture which it increasingly serves and which has systematically trivialized human feeling via serials and sit-coms, both televised and written.

The First Family has become soap opera. Chip and Caron Carter fail to hold hands a few times, and the whole nation rises to its feet, aghast.

"The people in the White House are real people," Lynda Robb says, "even though somebody wants to make them into cardboard figures."

At the same time that the coverage has increased, it is true, the presidential families have become more active, often viewing themselves as quasi-public figures. Possibly as a form of vaccination, the White House has taken to issuing its own bulletins about the family's activities. It is a way of fighting back, rather like Wilson Mizner eating crystallized ginger when he had an ulcer attack. This practice reached a peak of sorts when 9-year-old Amy Carter's doings were reported to the press corps.

First Ladies used to spend their time crocheting on the second floor or cutting ribbons, Carpenter observed, but now there are many opportunities for helping to spotlight an issue.

"The First Lady is an unpaid public servant," Lady Bird Johnson once said, "elected by one person: her husband."

The fascination with the President's family may have risen from an obsessive concern for the physical health of the President himself. This in turn, Carpenter speculated, may stem from FDR's death in Georgia and the fury of the press at being caught out in left field and at not having had a glimmer of Roosevelt's failing health during his fourth election campaign.

From then on, every time a President coughed it was news. Press secretaries were careful to give the public every scrap of information it could stand, right down to the quality of the great man's bowel movements. We have all learned a lot of medicine in the past few years from Eisenhower's ileitis and Johnson's gall bladder to Betty Ford's mastectomy and Rosalynn Carter's D and C.

Is there a solution? Not really.

"There used to be limits, but there aren't anymore. It's that address," Liz Carpenter said. "People identify with the First Family. Nobody who lives there really wants it, but it's very hard to avoid. They would be exposed anyway but it's always safer for the First Family to have some mission of good works, something purposeful. To give the press something to talk about besides a hairdo.

"It seems to me there should be some guidelines, like is the public interest concerned, and does the news have impact on the job of the elected official."

For Margaret Truman Daniel, the problem was minimized by the closeness of her family. She and her parents would talk about the latest invasion of their privacy and in most cases could laugh and forget it.

"I grew up in a small town," she said, "where everyone knew your business, so I was used to it. For me the worst thing about the White House life was the fact that I was there. I wanted to get out on my own, on my career."

As for the Secret Service men, they weren't so ubiquitous then. They would go with her on concer tours but not on dates.

"If my date couldn't take care of the situation, I'd say forget it - and forget him. I guess the family was more nervous after the assasination attempt on my father at Blair House. But we didn't mind the Secret Service. They were pleasant men."

One thing: She never opens a door unless she knows who's on the other side. She learned that when she was dressing for FDR's funeral and went to the door in her slip.

One other thing: While Mrs. Daniel isn't particularly interested in having her own children get into politics, she herself has joined the media. Her husband, Clifton Daniel Jr., is associate editor of The New York Times, and she has become a TV-radio celebrity as well as an author. ("I'm good at interviews," she said. "I can think of a lot of questions.")

Curious. Anna Roosevelt married a newspaperman, too. And David Eisenhower has been a sports columnist; Carolyn Kennedy was a newspaper copy aide; Lynda Robb writes for a magazine; Luci Nugent's husband is a cable television executive; Lady Bird Johnson has her television stations; Julie Eisenhower writes articles and books and appears on TV; Susan Ford is a photojournalist; Jack Ford is with Rolling Stone. Curious.