Republican Carol Schwartz had just finished her first debate of the campaign season with Mayor Anthony A. Williams, and reporters, as they often do, began clustering around the mayor with follow-up questions.

He was answering one -- and acknowledging a key point made by Schwartz that she and other members of the D.C. Council deserve more credit for improved city services -- when she swung around the corner into the bright spotlight of a television camera to press the point further.

"You do it in the campaign: You do 'I, I, I,' " she admonished the mayor as reporters watched. "The supercans were solely brought by me. The trash trucks were solely brought by me."

"I will say," added Schwartz, "I shared with you the trees."

The exchange highlighted the charged and highly personal nature of Schwartz's fourth candidacy for mayor, and her second against Williams (D). After months of resisting calls to run this year, Schwartz, 58, launched a belated but passionate campaign fueled by indignation at the mayor and a powerful longing to finally occupy the top job in a city that has been her home for 36 years.

Her list of complaints against Williams, 51, is extensive, and many are shared by her colleagues on the council. High among them is the mayor's personal style, which they say is frequently disengaged, prone to ethical stumbles and insufficiently collaborative.

As an alternative, Schwartz offers her relentlessly activist, energetic self and a "can-do attitude" about improving basic government services. It was her emphasis on such issues that motivated Schwartz to push for an expanded program of tree planting and the purchase of new "supercan" garbage cans and trash trucks, both of which have contributed to improved waste collection in the city.

She has been a consistent advocate of lowering the city's tax rates while pushing in many cases for better social services, including treatment for drug addicts. Schwartz, who is in her third council term, also has a progressive streak when it comes to social issues such as abortion and gay rights.

"She's a very sincere and caring person," said council member Sandy Allen (D-Ward 8), chairman of the Committee on Human Services. "She and I sometimes don't agree on tax issues, but as far as human needs for our residents . . . Carol has been very much in the forefront."

Her colleagues on the council, though sympathetic to many of her concerns about Williams, have not been willing to cross party lines to embrace Schwartz's candidacy.

The council's Democrats are backing the mayor, with varying degrees of enthusiasm. And the council's only other Republican, David A. Catania (At Large), said he will make no endorsement in the election.

Even so, as a group, council members speak highly of Schwartz. Their main reservation about her as a potential mayor is her limited background in management, they say. She has not run anything larger than her council office.

"Carol has strong leadership skills," said council member Jim Graham (D-Ward 1), who endorsed Williams, "but there is not that much in her background to indicate budget and administrative experience."

Schwartz counters that few legislators have executive experience before becoming mayors or governors, and she said that her years as a public official and community activist give her crucial expertise.

She moved to Washington shortly after finishing college in her native Texas, and her political career dates to the onset of limited home rule in Washington in 1974, when she ran for the school board. In the decades since, she has built a moderate record and developed a consistent ability to win supporters from the city's Democrats, who have a 10 to 1 edge in party registration.

"I don't care whether she's Democrat or Republican," said Lorraine Whitlock, a retired teacher who, like many supporters, speaks of a personal bond with Schwartz: "She's Carol." Whitlock was one of several dozen Democrats and independents who staged a rally at Schwartz headquarters last month.

She has won five elections, two for the school board and three for the D.C. Council, which by charter has two seats reserved for non-Democrats. Yet Schwartz has struggled to reach the higher posts she has sought.

Schwartz ran for mayor against Marion Barry, in 1986 and 1994, and four years ago against Williams. Her best showing, 42 percent, came in 1994, and her worst, 30 percent, was against Williams.

In each race, she promised a leaner and more responsive city government. "I look so forward to showing we can do it right," she said. "All I need is a chance."

If she wins this time, Schwartz said, she will make sure students get textbooks in the first weeks of school, even if she has to deliver them herself. She will demand that the city's thousands of police officers get out of their cars and walk their neighborhood beats. And she will personally drop by group homes and shelters to make sure that city agencies are properly treating those in their care.

"I've seen too many things that have made me cry," Schwartz said. "This is not going to happen on my watch."

She contrasts her record with that of Williams, who has repeatedly been investigated for ethical missteps, starting with his first bid for mayor in 1998. Just this summer, the election board denied Williams a spot on the Democratic primary ballot and fined his campaign $277,700 for submitting thousands of forged and fraudulent nominating petitions.

"Now we see that he is seriously flawed. Not only has he not delivered the kind of government we need and deserve, his ethical questions are mammoth," she said. "I'm scared for the future of this city. And as much as I want this job . . . I don't want him to have this job for another four years because I'm worried."

Schwartz's fears about a second term for Williams weren't enough to get her in the race this summer. As Republican leaders looked for a possible nominee, she repeatedly refused and counseled others that it wasn't worth the trouble at a time when Williams enjoyed strong poll numbers and what she says was uncritical news coverage.

She began to change her mind as Williams sank into the nominating petition debacle. Old supporters begged her to run. New ones, alienated by four years of Williams, urged her to give voters a choice in the general election.

And despite some discouraging signs, including the mayor's landslide victory in the primary, she began her campaign on Sept. 26, with less than six weeks to go before Election Day.

Since then, her all-volunteer campaign has opened a headquarters, raised $142,300 and picked up the endorsement of two unions, including the Fraternal Order of Police this week. No polling has been made public, but Schwartz says reaction to her candidacy convinces her that she has never been closer to becoming mayor.

"I will be devastated if I lose this election," she said.

D.C. Council member Carol Schwartz (R-At Large) is making her fourth run for mayor, an effort launched after the incumbent's campaign submitted fraudulent nominating petitions.