Patricia Malloy knows all about the revitalization in Washington's more prosperous neighborhoods. But in her housing complex east of the Anacostia River, she can see little improvement after nearly four years of Mayor Anthony A. Williams.

The streets are no cleaner, the recreation facilities no better, the community no safer, said Malloy, 52, head of the Lincoln Heights Resident Council. "Lincoln Heights needs more police officers," she implored Williams at a campaign stop in Northeast Washington this week. "I'm begging for help because we as innocent people need help."

Williams, 51, was eager to soothe her. "Sweetheart," replied Williams, who is not usually given to such affectionate displays, "we're going to take care of it." He even called the next day to get more information and assure her that he would speak to Police Chief Charles H. Ramsey about the matter.

But as Williams (D) campaigns for reelection and looks toward a second term, he faces much unfinished business and scant financial means to address it as the economy stagnates. Nowhere is the reality more stark than in places such as Lincoln Heights, where his accomplishments so far are difficult to detect.

That hasn't stopped Williams from sketching, in broad terms, an activist agenda for a second term. He pledged in a recent interview to focus at last on education, which he called "my biggest disappointment in the first four years."

He also vowed to deploy the city's uncommonly large police force in a way more visible to residents and less bound to patrol cars. And he predicted that the Anacostia River -- which is still polluted, despite his vow during his 1998 campaign to clean it up -- will begin to show signs of improvement.

Yet he acknowledged that each step forward will be made more difficult by the fiscal realities of a city with a limited tax base and rates that are already among the nation's highest. That threatens to leave him without a chief executive's favorite tool: new money.

"He's going to face a different city," said D.C. Council member Jack Evans (D-Ward 2), a leader on financial issues and a frequent critic of Williams. "It's easy to be on the council or in the mayor's office when times are good. . . . The question is whether the mayor is ready."

Williams said -- without a hint of self-doubt -- that he is.

In his view, he inherited a city government so profoundly broken that the uneven progress so far should be regarded as a triumph, plenty to earn him four more years to work on the areas that still cry out for improvement. Top on his list are the schools, whose funding grew under Williams until a month ago, when he and the council cut $30 million to help close a $323 million budget shortfall.

"The gravy train has wound down," Williams said, but he said the schools can perform better on the funding they have. "I don't think you need hugely vast sums of new money. We already spend a lot of money."

He said he has begun orienting his government to support the school system more fully, and he favors offering more social services at neighborhood schools to better prepare students for learning. His relationship with the District's school board has been strained, despite the new control he gained by successfully pushing for the power to appoint four of its nine members.

The mayor argues that there are ways to improve job training as well without busting the city's limited budget. And major projects such as the Anacostia River cleanup and several large new housing developments are bankrolled primarily by the federal agencies. Williams said he also will redouble his efforts in a second term to win an annual payment from the federal government of $400 million or more.

He also pledged a charm offensive after opponents in the primary election criticized him as being out of touch. He vowed to get around the city more and to listen more carefully to the concerns of residents such as Malloy. He said the intensive campaigning he has done since July -- when he was denied a spot on the primary ballot because of fraudulent nominating petitions -- will make him a better and more responsive mayor.

Even as he pushes these initiatives, Williams says that residents, particularly those in low-income areas such as Lincoln Heights, will begin to see the fruits of planning efforts that preoccupied him in his first term. A new grocery store in Ward 8, east of the river, is scheduled to be built soon, as are several new public housing developments.

"All these major initiatives in the city take time," said the mayor, asking for patience. "They're going to happen."

Not all of the city's political leaders share his enthusiasm for a second Williams administration. Republican nominee Carol Schwartz has warned that the repeated ethical problems from his first term are likely to recur, only with more serious consequences for the city.

Even some Democrats on the D.C. Council express little excitement about the prospect of four more years of Williams.

"I don't think he has the same passion for the city that Carol does," said council member Sharon Ambrose (D-Ward 6), who supports Williams and says he has a superior grasp of the economic issues facing the city.

Ambrose cautioned, however: "He has a lack of engagement in running the city, of getting down in the engine room. . . . He doesn't roll up his sleeves and get out there."

During the election season, that criticism has become a regular refrain from Schwartz and others, including Williams's leading Democratic primary opponent, Anacostia minister Willie F. Wilson. Several council members say that when they met with Williams during the budget crisis last month, he doodled and gazed at the ceiling as his chief administrator, John A. Koskinen, worked out a deal.

Such complaints visibly irritate Williams, who acknowledges that he can be easily distracted and sometimes fails to make eye contact. But his personal manner, however unconventional for a politician, is effective enough for him to produce improvements in city services, he said.

Schwartz and other critics question who deserves credit, but few dispute that many basic services, such as garbage collection and street maintenance, are better than when he took office nearly four years ago.

Polling by The Washington Post has shown that Democratic voters, who make up three-quarters of the electorate, regard city government as improved and put his approval rating at about 60 percent.

"People know," said Williams, brushing aside criticisms of his personality and his record as mayor. "They know that the city is improving."

Malloy is not sure that's true in Lincoln Heights. She voted for Williams four years ago but is undecided about whether to cast a ballot Tuesday -- even after he called her personally and vowed to help.

"Anybody can make a promise while they're campaigning," Malloy said. "I'm going to search to see whether I believe it's truly going to be carried out."

Mayoral candidates Anthony A. Williams, Carol Schwartz and Steve Donkin, representing the D.C. Statehood Green Party, appear at a forum this month. Williams has pledged to focus on education if reelected, calling it "my biggest disappointment in the first four years."Mayor Anthony A. Williams (D) says he inherited a city so broken that the uneven progress so far should be seen as a triumph -- and he should be reelected to continue the job.