NEW YORK -- Several weeks ago, Mayor David N. Dinkins took the podium in City Hall's ceremonial blue room and spoke eloquently about drug abuse.

"Today, we are raising in this city a lost generation of children," he said. "Some are born crack-addicted, others are traumatized by watching their parents shooting up or smoking crack and still others are stunned and squashed by the daily pounding of the drug-related crime that plagues their neighborhoods, their schools and their lives."

Dinkins had appointed one of his cherished task forces to study the issue and now was unveiling $9.8 million worth of pilot programs. There would be 1,340 new treatment slots for drug-addicted pregnant women, 80 for adolescents, a nursery for 20 drug-addicted babies and a small program for young probationers.

But with drug facilities available for less than 10 percent of New York City's 500,000 addicts, Dinkins was barely scratching the surface of a massive social problem. The "drug treatment on demand" that he touted during his campaign would have to wait, he said, "until the federal government gets serious about this issue."

Six months after taking the helm of the nation's largest city, the onetime Harlem lawyer is still struggling with a billion-dollar budget deficit that has tested his willingness to make unpopular decisions. Dinkins has moved swiftly to raise taxes while cutting into basic services such as fire protection, sanitation and schools, a process he has likened to "trying to decide which one of your children will eat less."

At the same time, the 62-year-old Democrat has spoken forcefully against the turbulent racial problems that helped him to oust former mayor Edward I. Koch (D). Confronted with rising tension about the Bensonhurst racial-murder case and a black boycott of Korean groceries, the city's first black mayor seemed immobilized at first, then suddenly found his voice and denounced some of the black activists involved.

The racial strife has turned Dinkins into a sought-after guest on national television shows, giving him a prime forum to criticize the Bush administration for failing to do more about drugs, homelessness and other urban ills. But those battles ultimately will be won or lost at home, and even Dinkins's supporters question whether he can stem the alarming decline in living conditions here.

"Given the lack of options, he's done really well," Bronx Borough President Fernando Ferrer (D) said. "He's been catching fastballs from the minute he raised his right hand to take the oath."

Still, Ferrer said, "If there's no activity in housing and education and so forth, all the wonderful speeches won't conceal the fact that nothing's happening. If you say you're committed to these things, you must find a way."

Investment banker Felix Rohatyn, chairman of a board that oversees the city's finances, recalled "concern that he would be soft on social issues and prone to big spending and borrowing programs. The financial community has been impressed that he hasn't done that and that he's faced up to these issues courageously."

Not everyone is so laudatory. Robert Hayes, chairman of Coalition for the Homeless, has accused Dinkins of "out-Koching the former mayor" by backing off his longstanding position that the city's barracks-like shelters should be closed in favor of smaller facilities for the homeless.

"We have been sorely disappointed," Hayes said. "He came in as someone who made a lot of promises to poor people. But with the financial crunch, he immediately began running to people who had a lot of anxieties about the David Dinkins who was going to give the town away."

By any measure, Dinkins has come a long way since November, when he defeated former U.S. attorney Rudolph W. Giuliani by just 42,000 votes of 1.75 million cast. Dinkins's victory was clouded further by two investigations into his personal finances, which since have fizzled. In a recent Daily News poll, 66 percent of those surveyed gave the mayor high marks.

A meticulous man who generally showers and changes clothes twice a day, Dinkins has ordered his bodyguards outfitted with black tuxedos, white shirts and cummerbunds for formal occasions. After 12 years under the combative Koch, many New Yorkers wondered whether the former Manhattan borough president could grapple with the conflicting demands of administering a $28 billion budget.

But when the city's deficit suddenly ballooned, Dinkins pushed through the largest city tax increase, $859 million in new taxes on income, property, gasoline and corporations. He also moved to delay hiring 2,200 police officers, close three fire companies, cut 417 parks workers, lay off 500 school employees and curtail after-school and summer-school programs. He bowed to pressure only once, agreeing to restore street-sweeping teams that he had abolished.

Dinkins weathered his first crisis March 25 when a fire swept through an illegal Bronx social club, killing 87 people. He visited the scene, spoke movingly about the loss of life and ordered a crackdown on unsafe clubs citywide.

As black-white tension increased this spring, Dinkins won plaudits for a dramatic television address in which he assailed "bigots" and "small-minded people" for whipping up racial hatred. Black activists were outraged, with the Rev. Al Sharpton saying Dinkins had "spit in the face of black people" and attorney C. Vernon Mason saying Dinkins had "no African left in him." But such attacks simply bolstered Dinkins's standing with mainstream voters.

"No politician likes to take on a member of his own ethnic group," one city official said. "When Dinkins did it, he opened himself to being dismissed as a Judas. I think it took a lot of courage to say what he said."

Dinkins scored a political coup when he played a leading role in the welcome of South African black leader Nelson Mandela. He also has embraced the role of urban advocate. When the U.S. Conference of Mayors met last month in Chicago, he called on the Bush administration "to stop treating American cities as though they were foreign nations seeking a handout." Earlier this year, Dinkins assailed the 1990 census for undercounting minorities, calling it "as bad as the early days of our country, when the census counted African-American slaves as three-fifths of a person."

Even while slashing services, Dinkins has set aside money for such small pilot projects as day-care centers to enable welfare mothers to obtain jobs, new teams of social workers to lure the homeless out of Grand Central Station, more counselors for troubled families and a program to turn five schools into nighttime recreation centers to keep children off the streets.

He also has moved some police officers from desk jobs to street patrol.

By targeting "high-risk groups" such as pregnant drug addicts, officials hope to "break the cycle of dependency," First Deputy Mayor Norman Steisel said.

"Some people would say we perhaps cut too far in terms of the traditional quality-of-life programs, parks and cultural institutions," Steisel said. "But the mayor says quality of life is affected by folks who have AIDS or who are homeless . . . as well as potholes and tree pruning."

Dinkins's incremental steps have enabled him to avoid the big-spender label. "The common denominator of the fears about Dinkins was that he would not represent the interests of the middle class," Republican analyst Jay Severin said. "But he's failed to do anything outrageous."

At the same time, Rohatyn and others warn that failure to address a continuing surge in crime, drugs and poverty could persuade more corporations to take their business elsewhere. "I would flat-out predict we're going to have the biggest exodus of businesses in the next couple of years that New York has ever seen, far bigger than in the mid-'70s," Staten Island Borough President Guy V. Molinari (R) said.

One insider conceded that city officials "have been so preoccupied with the emergencies of the day and week that they haven't been able to develop an agenda." This sense of drift has sparked complaints in the black community that Dinkins is neglecting his core constituency.

" "The mayor came in riding a wave of high expectations that all of us were concerned he would not be able to fulfill. People expected all kinds of miracles," said the Rev. Herbert Daughtry, a Bedford-Stuyvesant pastor. "What he has to do is rise to the challenge and make his presence felt."