At a citizens meeting last December, Fairfax County supervisor James M. Scott faced an angry crowd of constituents, who demanded that he either stop a low-income public housing project slated to go up next to their Circle Woods town houses or risk losing his seat on the county board.

The Providence District Democrat angrily rose to his feet and told them no. "I don't take well to threats," he said.

Later, Scott softened his stand on the issue, but performances like the one that night have won Scott, a balding and bespectacled man, a reputation for both courage and arrogance, and gained him both admirers and critics.

This year, Scott, 45, who is running for his fourth term, is under an aggressive and bitter personal attack from his Republican challenger, Steve Armstrong, a precinct captain for Scott in the last election who switched parties in 1981 after declaring that Scott had "lied" to him about a public housing project.

In his first bid for elected office, Armstrong, a flamboyant and, at times, abrasive attorney, is a sharp contrast to Scott, who speaks in a soft, slow, monotone voice and seems ill at ease with the hand grabbing, backslapping style of politics.

Armstrong, 50, and independent challenger William M. Lockwood, 57, a planner with the Army Corps of Engineers, both were spurned by Scott a few years ago when they sought political appointments, which Scott sees as the root of their differences.

Armstrong wanted Scott to appoint him to the county school board, but Scott turned him down. Lockwood, who served for 13 years on the county planning commission as the Providence District appointee of both Scott and his Republican predecessor, was turned down for a fourth term by Scott in 1981.

"Jim Scott did not see fit to reappoint me in the last go-round. He said it was time for fresh blood. Now I'm saying the same thing," said Lockwood, a square-faced man, with traces of a New York accent. Scott says that he refused to reappoint Lockwood because Lockwood had angered community groups with his support of high density development.

Scott also has gone on the offensive. He said that Armstrong's party switch means "you'll never be sure what he's going to do." And he accused Lockwood of "very bad judgment" in sending a zoning attorney a letter asking for support, attached to a copy of a planning commission action in which Lockwood supported the zoning attorney.

"Cheap shot," replied Lockwood, who said he has attached letters to anything from bowling score sheets to personal notes to remind people that they know him.

In his campaign, Lockwood has been trying to stake out the middle ground, between Scott, who has liberal support, and Armstrong, who has conservative backing. Armstrong, however, charges that Lockwood is really a liberal.

"He Lockwood lives in the Mantua area. The Mantua area has a small, highly active liberal community," said Armstrong. "If you hang around with ducks and you quack like a duck, you're a duck. If you hang around with liberals and you talk like a liberal, you're a liberal."

Scott, seen as the last remaining member of the liberal coalition that dominated the board in the early 1970s, was viewed as the most vulnerable supervisor in this fall's election. However, when Lockwood made the race a three-way contest, political observers predicted that he and Armstrong will split the anti-Scott vote and keep Scott on the board.

Public housing for the poor has emerged as a major campaign issue, in part because of Scott's consistent support of the Fairfax Redevelopment and Housing Authority, which runs the county's public housing, and in part because of Armstrong's aggressive opposition to public housing. There are fewer than 200 public housing units in the district, which has 79,635 residents.

Scott, who has raised about $11,000, says that he has spent a relatively small amount of time on that issue and that equal attention should be paid to his work on the neighborhood crime watch program, consumer issues, transportation improvements and parks.

Lockwood, who has raised about $7,000, has tried to steer clear of public housing, saying he supports adequate housing for all but that Scott should be more conciliatory in working with communities to locate the low-income housing.

Armstrong, meanwhile, has had to spend time denying that he is a conservative, although he acknowledges that conservative groups have backed him. During his primary campaign, Armstrong was touted by some as an anti-abortion candidate, a label that has brought continued controversy into the general election.

Last week, Armstrong refused to say where he stood on the abortion question. "It is not an issue that comes before the board," said Armstrong, who has raised about $3,000. "I'm not going to discuss it, just as I am not going to discuss the wheat sale to the Russians . . . . "

Providence District is located in central Fairfax County, extending from Falls Church to the Fair Oaks mall area and straddling Fairfax City. The district is one of the county's older, more densely populated areas, filled with numerous subdivisions and apartment buildings that went up in the 1950s and 1960s off of Rte. 50 and Rte. 29. Many immigrants from Vietnam and other Asian countries have settled in the area.

Armstrong says that one of his major issues is drug and alcohol abuse in schools. He says that even though this is an issue over which the board has no jurisdiction he will spend considerable time speaking out on the problem.

He also said the Fairfax government can decrease spending, decrease taxes and increase necessary services, by eliminating what he sees as wasteful services, such as the free videotapes that the Fairfax County libraries supply.

Lockwood says it is "unrealistic" to promise to cut total spending, although he said a lid can be put on the county budget. He said innovative policies, ranging from flexitime to four-day work weeks to Metro subway station shuttle buses, must be used to cut traffic congestion.

Lockwood said that streets near subway stations should get top priority for road funds, and that three-person commuter cars should be allowed on I-66 during rush hour to reduce traffic on Rte. 50.

Scott, a former chairman of the Northern Virginia Transportation Commission and a member of the Metro Board of Directors, agrees that transportation will be a major problem in Fairfax in the 1980s. He also said, if reelected, he would focus on other "quality of life" issues, such as education and excessive residential and commercial development.