In 1978, Linda Work was one of the many Ward 3 residents wearing buttons that said "Take a Stand with Marion Barry." Work, and others like her in the affluent swath of Washington west of Rock Creek Park, gave Barry the solid support he needed to eke out his narrow victory in the Democratic mayoral primary.

In 1982--last Friday night, in fact--Work donned a "Patricia Roberts Harris for Mayor" button, after listening to Harris field questions from a small group of Ward 3 voters who have become disenchanted with Barry's performance.

"You talk about a lot of things you want to do in the government," one man said to Harris as she stood in a living room on Windom Place NW in American University Park, a neighborhood of quiet, almost suburban streets and homes. "Barry said the same thing last time, but now he says four years wasn't enough. How long would it take you to get something done."

Harris laughed. "I thought you were going to ask me how much I could get done in the first year," she said. "My experience is that people set the direction of an administration in months, not years . . . . We can get control of crime, support for the victims of crime, and reorganize the budget in a matter of months."

After Harris had finished speaking, Work said she is going to vote for her in the Sept. 14 Democratic primary. It is through convincing voters such as Work that she can succeed where Barry failed that Harris has opened up a substantial lead in what used to be a Barry stronghold.

"I guess I voted for him Barry because I felt the city was not well managed," said Work, a mother of three who has lived in the city 17 years and has an 8-year-old in Eaton Elementary School. "It's still not well managed. As a consumer of government services, I can't get a response unless I call the mayor's office. Dealing with the agencies is a real horror. He hasn't performed."

Work said that Harris, on the other hand, has been impressive in talking about how she would manage the city's bureaucracy and budget. "She says it's not mystery or magic. We can determine what our obligations are and what our revenues are. I like that."

Ward 3 was the only ward in the city where Harris led Barry in a recent Washington Post poll, with 41.9 percent of the support of those polled as opposed to 37.6 percent for Barry. Barry led Harris citywide by 13 points, with the other candidates in the race--John Ray, Charlene Drew Jarvis and Morris Harper--far behind.

In addition, Ward 3 gave Barry his highest unfavorable rating in the poll, with 42 percent of those interviewed saying they dislike him--eleven points higher than in any other ward in the city. Twenty-two percent of the people polled in Ward 3 said they would not vote for Barry under any circumstances.

Harris' lead in the ward, which includes all of Washington west of Rock Creek except Georgetown, has become a matter of concern for Barry, who now calls the ward a political "battleground" in the primary.

"We pulled 47 percent of the vote in Ward 3 in 1978," Barry said in his downtown campaign office recently. "I don't know about doing that this time. Part of what's happening . . . is a certain amount of anti-incumbent sentiment . Just anti-whoever the incumbent is. But we hope to do well, we're going to take our case to Ward 3."

Strategists in both camps think that if Harris is able to replicate Barry's success in Ward 3 in 1978 and build a large lead, she could offset Barry's large lead in Ward 7 across the Anacostia River, and possibly win if she can edge out Barry in a few of the remaining wards in the city.

Harris has already copied Barry's successful 1978 strategy for making inroads into Ward 3. Unlike the situation in other wards where poor city services, lack of jobs and housing problems are all key concerns, efficiency in government seems to be far and away the dominant issue in Ward 3.

Delays in getting permits, being put on hold when calling a city agency, and slow return of tax refunds are often-heard complaints of voters who say they will not vote for Barry this time.

"Ward 3 understands that we deserve to have a quality administration," said Harris. "A number of people supported Marion Barry with the hope of improving administration of the city government. They see he has not delivered, they see the incompetence, and by and large they don't buy the argument that he can't do better because Congress interferes . . . they aren't convinced by his excuses."

Ward 3 is demographically unique in the city: It is about 95 percent white, while the remainder of the city is over 80 percent black.

Harris plays down the idea that her principal support is from whites. "They in Ward 3 are similar in outlook to people supporting me in other wards," she says. "The key question for them is the quality of city services, not race. My political support is across the city."

Politically, Ward 3 is the most varied in the city, with 23 percent Republicans and 20 percent independents along with its majority of Democrats. In the 1978 general election, won by Democrat Barry with a 2-to-1 margin citywide, Republican Arthur Fletcher mounted a serious challenge and came within 1,035 votes of beating Barry in Ward 3.

The largest Republican parts of the ward are in the Palisades and Spring Valley, with the American University Park and Wesley Heights areas split between Republicans and Democrats. The largest Democratic precinct is in Glover Park, with Cleveland Park and Chevy Chase also heavily Democratic.

One negative for Barry in the ward is that much local political activity in recent years has centered on battling him to keep the school budget intact despite citywide budget cutbacks.

A potential plus for the incumbent is that Ward 3 has the city's largest population of people aged 65-84. Barry has worked to attract votes from senior citizens with a citywide discount card program for the elderly other special programs, earning him the support of voters such as Ruth Haugen, the city's representative to the 1981 White House Conference on Aging, who says Barry "has done a great deal for elderly."

To battle Harris, Barry has set up a campaign office in the ward and is traveling there regularly, working the Wisconsin Avenue waiting line for the movie "E.T.," riding in the lead car at the Palisades Civic Association parade, shaking hands at the Johnson Flower Center, handing out flyers at the Cleveland Park subway stop.

As in most of the wards, Barry has won the support of top political leaders. Barbara Baldwin, head of Ward 3 Democrats, is Barry's campaign coordinator in the ward. Barry's biggest supporter in the ward is longtime council member Polly Shackleton, now in a heated fight for her own reelection.

"It's still a tight race, I think," said Shackleton. "He has 80 to 90 percent of the Democratic leadership with him, but the voters . . . some people expected everything to change overnight after Walter Washington. There have been problems and there continue to be problems, but no one can perform miracles."

Much of the battle between the two front-runners is being fought in small meetings at private homes in the ward. Barry has been at the home of Harold Himmelman, a strong Shackleton supporter; at the home of John Hechinger, the president of the home-supply-store company; and at the home of Sally Craig, the president of the Eaton school Parent-Teachers Association.

Harris, meanwhile, has been making her own rounds of meet-the-candidate sessions, attending 31 "coffees" in the ward since February.

"Pat has been in Three as much as any other ward," said Mary Ann Keeffe, Harris' ward coordinator. "And it's paying off. I think her lead is growing. It's much more substantial than it was in the poll."

Both sides say they are awaiting The Washington Post's campaign endorsement. Barry won that endorsement in 1978, and it was widely viewed as important to his success in Ward 3.

But for now, he is an underdog in the ward that four years ago carried him to victory.

"I've seen them both now," said a woman who asked not to be named after listening to Harris recently. "Barry is a great campaigner. He's a smooth cookie. But I've heard those lines before. I'm not buying it this time."