Lenny Skutnik, who dove into the ice-choked Potomac River Wednesday to save the life of a drowning woman following the jetliner crash in the Potomac, has had little experience in the hero business.

Skutnik, 28, whose full name is Martin Leonard Skutnik III, is experienced in less exalted matters. He's been a meatpacker, house painter, furniture-plant worker, hamburger cook and strip-and-wax man at Ralph's supermarket in Simi Valley, Calif.

Skutnik now works for the Congressional Budget Office, where he runs errands, delivers mail and makes $14,000 a year. A big night out, Skutnik says, is taking his wife, Linda, and their two sons to Brothers Pizza near their $325-a-month rented town house in Lorton, Va. "Every once in a while we'll close our eyes and blow a couple of bucks," he says.

The only other time in his life that he had a chance to be a hero, Skutnik says, he flubbed it. He was anchoring a relay team in a high school race and he could have won the race, but he pooped out and stopped. The coach yelled at him: "You quit, Skutnik. You quit."

Late Wednesday afternoon, as one of hundreds of homeward-bound commuters drawn to the banks of the Potomac by the crash of Air Florida Flight 90, Skutnik, who's never taken a life-saving course, saved a woman who was too weak to grasp rescue rings lowered from a hovering helicopter. Television spread pictures of his valor to the nation.

President Reagan, in a speech yesterday in New York, spoke of Skutnik's bravery: "Nothing had picked him out particularly to be a hero, but without hesitation there he was and he saved her life."

Interviewed yesterday at his home 20 miles south of the 14th Street bridge, Skutnik could offer no fancy explanations for risking his life. "Nobody else was doing anything," he said."It was the only way."

The woman Skutnik rescued apparently was Priscilla Tirado, whose husband and infant son perished in the crash. Skutnik was sure yesterday he had rescued Kelly Duncan, an Air Florida stewardess, because a woman who identified herself as Duncan's roommate called from Florida to thank him. However, an Air Florida official said last night she had talked to Duncan, who remembers being pulled to shore by a helicopter. Tirado's father said family members recognized his daughter on television as the one Skutnik pulled to safety.

After the rescue, as he waited in an ambulance that had run out of blankets, Skutnik gave his coat to Joseph Stiley, a survivor of the crash who had two broken legs and was shivering. Shirtless and shivering himself, Skutnik, who lost his watch and a cap in the river, was taken to National Hospital for Orthopaedics and Rehabilitation in Arlington for treatment of hypothermia. He didn't want to go.

"I'd heard all these horror stories about hospitals and all the forms. The first thing I said when I got there was 'Is this going to cost me anything?' " said Skutnik, who's described by his colleagues at CBO as an exemplary worker.

He was dispatched, free of charge, to a hot tub in the hospital to soak for 40 minutes and warm up.

When Skutnik got out of the tub, he faced reporters--scores of them, frenzied and facing deadlines. They pushed and shoved to ask him what "it felt like." He had never met a reporter before. He told his story again and again.

Back at his town house at 10 p.m., before Skutnik could get home, a woman from ABC's Nightline show arrived in a limousine and told Skutnik's wife that Lenny was scheduled to be on the show that night. "The woman a secretary at ABC named Cynthia Dowling said she may lose her job if Lenny didn't go on the show because ABC had already told 20 million people he'd go on," Mrs. Skutnik said yesterday. She said that the secretary told her that Lenny had promised to be on the show.

Mrs. Skutnik called her husband, who, on his way home from the hospital, had stopped off at his father's home in Springfield, about five miles away. Mrs. Skutnik says she told Lenny on the phone that Nightline was waiting for him. But Skutnik, exhausted from his brief swim in the Potomac and from countless interviews, says he told his wife he didn't want to talk to Nightline. Skutnik, who says he made no promise to do the show, said yesterday he decided to go on Nightline when he heard that the secretary might lose her job.

Ted Koppel, anchor of the Nightline program, said yesterday that Dowling, a new employe at ABC, had been joking when she said she would be fired. "Cynthia said it the statement about her being fired was said in a joking way," Koppel said. He said that Mrs. Skutnik laughed at the joke.

"I can't emphasize strongly enough that that is not the kind of thing we would do," Koppel said. The Skutniks yesterday said they did not take the secretary's remarks as a joke

As for the television appearance, Skutnik said yesterday: "I was nervous. I was tired. I didn't know what I was."

Skutnik's instant celebrity began Wednesday afternoon near the 14th Street bridge when traffic in the express lane he was car-pooling home in came to an abrupt stop. Skutnik followed scores of stalled commuters down to the river, where there was a rumor that someone had been hurt. He said he didn't hear the metallic crash of the plane and the bridge.

From the shore, Skutnik said he saw the partially submerged plane with a half dozen passengers clinging to it. He saw one spectator tie a rope around his waist and attempt a rescue.

The man who tried to swim out to the wreckage was Roger Olian, 34, a sheet metal worker from Arlington, who was drawn to the accident after getting caught in traffic near the bridge on his way home from work.

"I went in with a make-shift rope that kept getting stuck on the ice," Olian said yesterday. "I was about five feet from the plane when the helicopters arrived. But by then he'd been in the water more than 15 minutes I'd just about had it. I nearly sank, but they pulled me in," said Olian.

Later, when it became obvious that a helicopter could not save the drowning woman, Skutnik said he didn't have any profound thoughts. "I just did it," he said. "When I got out of the water, I was satisfied. I did what I set out to do."