Shaun Cassidy couldn't quite find the words to describe how he felt meeting President Carter at the White House yesterday. He made a few tentative tries, thought about it awhile, and finally, his big, brown, Liza-Minnelli eyes open wide, he came up with the perfect description.

He said, "I felt the way people feel when they meet me."

Cassidy, who is a TV star, a maker of hit records, and an unforgivable and ebullient 19 year old, wasn't bragging. He was understating. When people - well, girls - meet, even glimpse, Shaun Cassidy, they go helter skelter. They freak. Tehy squael and jitter. Shaun Cassidy has replaced Peter Frampton as the new national male nymph.

He is the masculine equivalent, and the fan magazine costar, of Farrah Fawcett-Majors. He wrote a song called "Teen Dream" and he is; it was in his second album, "Born Late," and he was.

"I wish I were older; I'd feel better about this," said one of four White House secretaries waiting for Cassidy to finish his tour so they could get his autograph. "This is for my niece, she's a little girl," the woman said. And then she got a gander at SHAUN, who materialized in a hallway near the press room. He was wearing a perfect three-piece brown suit and flashing that deservedly celebrated baby-fat smile and the woman shouted, "Oh, he IS cute!"

The White House went crazier over Shaun Cassidy than Shaun Cassidy went over the White House. While attempting to eat a cheeseburger in what they call "the White House mess," as a guest of a staff member, Cassidy was called upon to sign "stacks and stacks" of autographs, one secretary said - "more than I've ever seen anybody asked for in there."

The thing about Cassidy's constituency is that it starts very young and goes very old; Amy Carter, 10, who didn't get to meet him until before his sold-out concert at the Capital Centre last night, is among the legions.

They watch "The Hardy Boys" on ABC, these legions, only to see him, and they pack huge arenas (average capacity: 18,000 people) in order to be driven to frenzies. Should he lose them, even for an instant, which is unlikely, all he has to do is turn around and wiggle.

It could all be so demoralizing if it weren't all so wholesome. People who think they'd love to hate Shaun Cassidy had better not meet him, because then they would be undone.

He has an immobilizing charm. Skepticism crumbles before it. When he walks through the hallways of his hotel, near Dulles Airport, there are girls around every corner with cameras poised - one thinks of a potential fate traveling an obstacle course lined with snipers - but Cassidy remains a kind of floating peace center.

"I just don't take it all very seriously," he says, later, flopped on a bed in his room. Crowds of 18,000 people shrieking at every little movement don't bother him? "I'd be very nervous if it were 100 people. Then I could literally look into everybody's eyes.It's a scary thing, to look at them, right in the eye. Like, you'll look at a young girl, right in the eye, and she gets a little spaced out, and then you look back a second later and see she's totally freaked by it.

"Also, I try not to look at just one person a lot, because I feel that's cheating everybody else."

A kind of chaperone-bodyguard, Fred Westheimer,has left the White House with envelopes full of souvenirs. "Catch the matches," says Cassidy to a member of Virgin, the opening act in his show (the ads say, "SHAUN CASSIDY - Virgin," but don't ask).

At the White House, "I hugged Rosalynn," says Cassidy, grinning wide as if hogging a camera. He doesn't quite remember what he said to President Carter. "He's really mellow, though," Cassidy says. "And there's a warmth there. I think of myself as soft-spoken. But boy, he was really soft-spoken. And he was Real. Which was nice."

They probably shoot him full of lithium," says the musician, a cynic. Westheimer wonders if there might have been a sprinkle of Valium on the President's lunch. Cassidy laughs but he does not join in any of this disrespectful wisecracking. He either has great tact or great show-biz manners - probably the latter, since his mother is Shirley Jones, his father the late Jack Cassidy, and his half-brother David Cassidy, whose fame Shaun has totally outdone and eclipsed.

"See, all this hasn't altered my life that much, because my family was in show business, and I always felt like some kind of celebrity anyway," Cassidy says. "When I was 5, I was on the road with my mother when she did summer stock. I'd go on stage in small parts. What did I play? I played a lot of midgets."

About a year ago, Cassidy moved out of his parents' house and into his own place in the canyons of Bel-Air. His records and TV show bought it for him; the two albums have each sold 2 million copies and he's had three "gold" singles as well. Cassidy's record sales are as big or bigger abroad - in England, Germany and other countries - as they are here. He is, a Warner Bros. Records spokesman confidently declares, "a millionaire."

Now the celebrity life is escalating for him. He leaves restaurants and finds hordes of photographers trying to find out who he had dinner with because "the restaurants phone them and tell them I'm there to get publicity for themselves." Such are the rites of ascension in America.

To get away from such pressure, he says he goes bowling, to movies like "Annie Hall" and "Close Encounters" and he plays pinball. "Pinball is great therapy. Everything phases out. Even if everybody is watching you."

He's debating now whether to move on the grounds that his house is too "accessible" and ponders "getting reclusive, with gates and dogs and the whole bit." It will probably come.

Cassidy sells a lot of records. That doesn't make him a great singer. But he is a terrific performer; there's something so touching about the way he goes all out, about how hard he tries. The night after Cassidy stole the show on the Grammy Awards, a cab driver offered an unsolicited critique: "Those Grammy Awards were terrible. The only good thing on the show was Shaun Cassidy. That kid sang his little heart out."

Cassidy, who plays drums, guitar and piano "with varying degrees of proficiency," says, "I don't think of myself as a musician at all. But after the Grammys, real musicians like George Benson were coming up to me and telling me I was good, and that was terrific. Suddenly I knew I was doing it for something other than just for me." He smiles. "I guess it is for me in the long run, anyway, but it was great to hear that from somebody like George Benson.

"Rolling Stone seems to like me, which kind of surprises me. They have an interview with me coming out soon. What people's opinions are of me I don't really mind, but I do get upset when people say what I do is "Bubble Gum Music." I don't like bubble gum music. People forget what the term means - it started in about 1971, with songs like, 'Yummy Yummy Yummy, I've Got Love in My Tummy,' songs that actually mentioned candy and gum.

"Well, I've never make a reference to gum of any kind in any of my songs."

Cassidy writes about half the material in his albums, the third of which will be out in June. "I'm very influenced by the music of the early '60s, a real rock 'n' roll freak," he says. "I love Phil Spector and the Wall of Sound, and Lesley Gore, and big production. It's all become very mechnaical now, so I try to put a little more juice in my records.

"I think music needs a slap in the face. The public needs a slap in the face. I'm not the one to do it; I don't have some big Master Plan. But you know, punk came along, and it fizzled pretty quick, but the idea that people wanted something new was good. I think something very revolutionary is going to happen soon."

Cassidy is in the back seat of a limousine now, one that had to be jump-started in the front driveway of the White House - though not, thank Good, while he was in it - and suddenly he asks for a cigarette. And as he lights up, he realizes that an illusion held by someone else in the car has just been jolted.

"What's the matter - am I ruining my image?" he asks, after a puff. "It's okay. The kids know it too." Oh. The kids know it. But doesn't he feel the obligation to lead, at least publicly, a - "a moral life? Yes. I don't take drugs." So he's antidrug? "No."

Cassidy doesn't know at this point whether ABC will pick up "The Hardy Boys" for next season. He seems to hope they won't. "It's not really a good show. They could make it better. I don't want to knock it; it's helped me in a lot of ways, and I do the best I can.

"The ratings went up when I sang on the show, so they wanted me to sling every week, but I said no. They just wanted to tack the songs onto the end of the show. I said, 'There has to be a reason for me to sing.' We have to be investigating a discotheque, or something."

It is obvious, as it was with Farrah, that Cassidy is quickly going to get too big for the confines of "The Hardy Boys," which is confinement itself. On the bulletin board in NBC programmer Paul L. Klein's office is a little white card that says "Shaun Cassidy." That means he is set to do a variety special sometime next season. Could this not turn into a weekly musical-variety series? "I don't think so at this point," Cassidy says. "Variety television is pretty terrible. In fact, television on the whole is pretty crummy. And it destroys your record career if they can get it for free."

If that sounds calculating, it's probably misleading. Cassidy does not seem consumed, even entraced, by his fabulous success and the ardor of his followers. "I worry for them sometimes, more than for myself, because when I'm on stage, I have protection and they don't. You just try to understand it all as best you can. I mean, the White House today - why was I there? Because I'm on a TV show? Because I make records? It's as mind-boggling to me as it is to everybody else. The thing is, you can really have a lot of fun with it, and right now I am. The things I did today were great."

This kind of ingenous enthusiasm is unassailable. Cassidy tries to describe the White House for the musician in his hotel room and he becomes a more-or-less typical American kid: "There was always a fresh stack of wood in every fireplace, like it was ready to burn" . . . "I sat in the President's chair in the Cabinet Room" . . . "He just seemed spaced out on how nice the garden is" . . . "The security is fantastic . . ."

You can't fight this. It's not talent necessarily or genius or exploitation of our need for idols. It's that Shaun Cassidy, hot number and quiet kid, seems to deserve his success by virtue of having not let it drive him crazy. It's everybody else who is driven crazy. "This is Shaun Cassidy," he said on the phone to room service, obviously relishing the gasp at the other end and a little later, the girl from room service arrived with a tray on which the Cokes and the hot tea and lemon jiggled nervously.

Later, a guard posted outside the door roars, "You should have seen that girl from the room service when she came out of that room! She just leaned back against the wall with her mouth open! It was like she was in a trance! Wow!"

"It isn't just kids that come to see me," says Cassidy. "There are people older, and my age. Fathers come in there, with their daughters, and they sit there with their arms crossed like they're expecting some ghastly rock and roll craziness. But after awhile the majority of them are really into it. And then I look at the mothers, and the really get into it, too.

"But then the mothers see the fathers looking at them, and they sit back all of a sudden, like they aren't into it any more."