Dora Woods, comedian, stood at the mike sweating. To her left was a group of onlookers and a harried chap with a clipboard; to her right, three tourists lay flushed in the grass. And in front of her was no one--save a grim-looking TV cameraman and the stone-faced Washington Monument rising up behind him.

"Last year I was in Mexico City for the Kaopectate Festival," Woods began haltingly, her eyes darting left, right and center. "I sure made a run for it." The roar of an approaching jetliner threatened to drown her out. "You know," she braved onward, "I just had plastic surgery the other day. My husband cut up all my credit cards."

A comic on the sidelines shook his head. "Welcome to Comedy Hell," Neal Graham said. "I mean it."

Yesterday, Woods and Graham were among 30-odd comedians who offered themselves up to the Showtime cable television service as "The Funniest Person in America." They came to do their routines, in blistering heat, from a platform protruding from a Superior 2900 recreational vehicle with videotape machines and monitors.

Obstructing the Superior's windshield were gigantic inflatable Groucho glasses, the moustache brushing the bumper, and the "Showtime" logo blazoned in red above the wheels. "The Funniest Person in America," screamed writing along the sides. "You could be it!" shouted a legend at the rear.

It was enough to lure humorous beings from as far away as Richmond, plus such journeymen of the Washington scene as lawyer Dan Brenner and Reagan impersonator Jim Morris. They kibitzed, quipped and traded business cards in the shade of the Sylvan Theater, and silently pumped themselves up to face the cold camera. "DC's Funniest Comedian-Impressionist," one comic's card read, while another funnyman--himself quite a card--sported a T-shirt reading "Comedians Do It Standing Up."

And from Beltsville, the spectacle drew Dora Woods, the stage name for a redheaded grandmother of seven, who turned out in a print blouse and brown double-knit slacks. She retired a few years ago as a clerk-typist for the U.S. Department of Agriculture and has become a regular at Garvin's Laugh Inn on open-mike nights.

"I usually don't go over very well," she said, shaking like a woman in a Siberian blizzard as she scrutinized a sheaf of papers filled with pencil scrawls. "I always get this nervous. I remember the first time I tried this, I was razzed and booed so much, I thought the building was going to vibrate apart. I've never really had a good experience. I use some jokes from Henny Youngman, but most of the material is mine. I sold two jokes to Joan Rivers once. She paid me $10 apiece."

"I bet Dora will get onto the Letterman show before any of us," ventured ventriloquist Richard Paul, who showed up at 10 in the morning after breakfast with his Ronald Reagandummy at Garvin's Laugh Inn. "I predict she'll end up having a cult following, just like 'The Rocky Horror Show.' "

If she's lucky, she might turn up in one of eight short shows that Showtime will cull from some 150 hours of tape: mainly stand-up routines and footage of host Adam Lefever in such jolly pursuits as restaging the Bastille Day waiters' race at Dominique Restaurant, or interviewing Milton Pitts, President Reagan's barber.

They'll be aired in the next few months, between full-length movies and made-for-cable series, as "continuity programming"--which is televisionspeak for filler.

But if Dora Woods is the luckiest one of them all--that one out of thousands whom the experts certify as "The Funniest Person in America"--she'll win a month-long stint on Showtime's entertainment schedule.

"We're pretty serious about finding the funniest person in America," said the project's executive producer, Josh Sapan. "This is probably the most extensive nationwide comedy search in history," he said. "It may well be the only one in history."

Yesterday's joke-athon--emceed by hosts from Washington's all-comedy WJOK-AM radio station--was launched by Tom Wheeler, director of the National Cable Television Association. He worked a giant scissors to cut a red ribbon in front of the Groucho glasses. First up was Vincent Cook.

"Good evening," Cook began, shading his eyes from the sunlight. After a few long minutes, he ended glumly, "I enjoyed doing what I just did--which was basically nothing."

Then one comic after another told jokes about poverty, plane crashes, cockroaches, bar mitzvahs and venereal disease. One young man did his impression of Luciano Pavarotti selling tight underwear, and another spent his whole routine impersonating retired boxers.

Tommy Lyness, a construction worker from Baltimore, waited edgily to go on. He had called in sick to his job so he could perform on camera in Washington. "Well, I am sick," he said. He paced the grounds with a rubber dove on one shoulder, a bird cage on his head.

Jim Morris, doing Reagan, announced a new Pentagon program to develop "multiple punch line jokes, surface-to-air jokes, land-based jokes and the neutron joke. That one leaves the room standing but it kills the crowd."

"It's a great pleasure to appear on America's first nonprofit pay cable service and in the 15 or 20 homes that subscribe to it," said Dan Brenner. He added, "I celebrate the three great Jewish holidays: Rosh Hashana, Yom Kippur and the Academy Awards."

The Showtime network, which actually serves about 4 million households, embarked on its quest for mirth on July 28 in New York, with plans to visit 16 cities from Boston to Seattle. For the two camera crews driving the 7,000-mile route, it's an odyssey of hilarity lasting 34 days.

"It's our own version of 'No Exit,' " said Jim Hayman, a cameraman. "I'm cracking up right now," he added, not even trying to smile. "I would say that by now, we have heard more than 10 jokes," said Jon Brandeis, the field producer. Thousands? he is asked. "I'd just say more than 10."

George Monas, the soundman, sat in the Superior 2900, swishing an outsize fly swatter at the comic who happened to be on screen.

"I haven't used this on any of them yet," he said, a dazed glint in his eye. "But wait till we get to Oklahoma City."