"IT'S THE GRANDEST HOUSE we ever had. When Eleanor had twelve high school girl friends over for a slumber party, we couldn't even hear the gigles," said Joan Mondale, as she gave an enthusiastic tour of the Vice President's House the other day.

She likes to call it the Vice President's House, not residence.

The Mondale insistence on the less high faluting term tells much about the Mondales and the problems of being a populist who's been elected to the elite.

The Mondales obviously enjoy the grand house. ("It's wonderful for everyone to have their own space," Joan Mondale said.) They are rightly impressed by it. ("We could put our Cleveland Park house on just the first floor of this one," she said with some exaggeration.)

But they don't want anyone to think they're putting on airs, so they have brought their own down-to-earth personal style to the grand house, complete with a vegetable garden on the south lawn, membership in a food co-op, family errands run by Joan Mondale and the children, and ashtrays made by Joan Mondale and her teacher, Vally Possony.

Mondale has put together, with the help of an old friend, Martin Friedman, director of the Walker Art Center, Minneapolis, a year-long sampler of American art of today, fifty-two paintings and sculptures, borrowed from museums in her own mid-west. Art historian Joan Mondale's grand plan is to turn the Vice President's House into a showplace of American contemporary culture, the only government setting for official entertaining amid the best of America's current arts and crafts.

The house is on Observatory Hill, overlooking Massachusetts Avenue, surrounded by twelve expensive acres, cared for by the Navy. Navy stewards also serve in the house.

The 1890 brick house, designed by Washington architect Leon Dessez, previously was known as "the Admiral's House" and was the residence of the Chief of Naval Operations.

Its curving wood veranda in the southern manner makes you think of full skirts and porch swings. The house has all the other amenities of its period: twenty rooms with 11 1/2-foot ceilings, funny gables with roof overhangs that look like wide-brimmed hats, and the three-story mandatory turret.

One ordinary afternoon, Eleanor, 17, the only Mondale daughter, walked up the hill from school, stopped to talk with the Executive Protective Service guards in the tiny guardhouse sprinkled across the grounds, and took a sun bath on the deck. Later, she came into the sitting room and talked with visitors, taking her socks off because her feet hurt.

"I like living here. But I miss being able to just go across the street to see my friends. When they come, we have to call and leave their names at the guard gate. It's sort of lonesome.

"I have the best room on the third floor. I have the tower room, because I came with my parents before my brothers."

The children are making their mark on the house. Eleanor's art class at Georgetown Day School is making two murals for the third floor. Teddy, the 19-year-old son, has his dirt bike trophy on the highly polished sideboard in the dining room. William, 15, races up the main staircase as if he had always lived there.

The art work with its brilliant colors and surprising shapes has given the house and its neutral furnishings a completely different look: cheerful, brighter, more intimate.

Currently, as a part of her American art showcase design for the house, Mondale is adding a collection of craft objects.

But it all takes time, and if the house now has a rather naked newness to it, Mrs. Mondale and her family are settling in as if they expected to stay for a while. After all, it was a mid-western versifier who said, "It takes a heap of living to make a house a home."