Finally, like a glowering patriarch, he lectured and scolded them, threatening to leave. “This means you will live forever in poverty!” he exclaimed. “If we do not listen to each other, how can we fix anything?”

Suddenly, the rage of the throng dissipated. There was a chorus of apologies. A voice shouted, “Sorry, Baba!” Then a cry arose for the president to sing his trademark song from the anti-apartheid struggle, “Bring Me My Machine Gun.”

“You want it?” he asked.

“Yes!” they shouted. And like an aging entertainer obliging with a golden oldie, Mr. Zuma, 68, crooned and boogied onstage.

It was a moment that encapsulated both the promise and the unfulfilled potential of Mr. Zuma, who has raised the hopes of the dispossessed but not yet delivered the better life they are demanding. Despite persistent corruption charges and the taint of extramarital affairs, he is a political survivor who has risen to lead the continent’s powerhouse nation and will soon step onto the international stage as South Africa holds Africa’s first World Cup.

With his rumbling laugh and habit of dancing onstage, Mr. Zuma has a gift for connecting with the country’s impoverished black majority, who are impatient for the better life promised by the dawning of democratic rule 16 years ago.

“I’ve never seen a president in Africa in direct dialogue with his citizens like Jacob Zuma,” said Zakhele Maya, 26, an activist in Siyathemba who, like most in the township, is jobless.

But that connection has not quelled the discontent. After an earlier visit, last year, Mr. Zuma ordered the government to improve the township’s health and housing services, yet frustrations continued to rise. In February, residents burned down the library. The books are now charred scraps, the library a pile of blackened rubble.

A year into his five-year term, Mr. Zuma recently signed performance contracts with his ministers, setting out specific results for them to achieve. But analysts are urging action, not aspirations, on South Africa’s core challenges: a failing education system, staggering levels of joblessness and the widening chasm between rich and poor. There is already open speculation about whether his party, the African National Congress, in power since the end of apartheid, will pick him for a second term.

“By 2013, the questions arise: Who will govern beyond 2014?” asked Trevor Manuel, who heads the National Planning Commission in Mr. Zuma’s office and was finance minister for the previous 13 years. “And the intense period has to be 2011, 2012, into 2013. Those are the middle years of the term of government, and I think the foundation is now well laid. Now you’ve got to drive the change.”

Mr. Zuma’s highly personal, consensus-building style has helped him lead a sweeping new attack on AIDS after almost a decade of failed leadership under his predecessor, Thabo Mbeki. But even some in his party say that tackling the nation’s deep economic problems will probably require angering allies who put him in office, especially Cosatu — the powerful trade union federation that is part of the governing alliance — and the A.N.C.’s youth wing. It is led by the incendiary Julius Malema, 29, regarded by many here as a demagogue who plays on racial antagonisms and who was recently sent to anger management classes by the party.

The dry kindling of resentment is here to be ignited. The ranks of the jobless have grown by more than a million in the past year and a half, and South Africa, population 49 million, already had among the highest rates of chronic unemployment in the world. More than a third of the work force, including those too discouraged to seek work, is jobless. Studies have found that most of the unemployed have never held a job.

Mr. Zuma announced in February that proposals would be put forward to subsidize the wages of inexperienced workers, to help them get a foot in the door. But Cosatu, the Congress of South African Trade Unions, which represents those who already have jobs, opposes the idea — and debate within the government continues.

Another point of tension is education. Last year, Mr. Zuma said teachers and principals — whose union is also part of Cosatu — must be held accountable for whether they show up and do their jobs. In an interview, Mr. Zuma reiterated the need for such a step and said it would be taken by the end of his second year in office.

“There’s no teacher who’s going to hide behind the school,” he said.

But critics question whether Mr. Zuma has the support to follow through on these difficult decisions, the vision to address the country’s daunting challenges or the standing to root out corruption. Worries deepened when it surfaced that Mr. Zuma, who already had three wives and a fiancée, had fathered a child, his 20th, out of wedlock with the daughter of a family friend.

“The biggest danger we face as a country is the use of office for personal gain, and it is becoming so, so normal, and nobody’s arresting that,” said Mondli Makhanya, a newspaper editor whose reporter broke the story about Mr. Zuma’s child in The Sunday Times. “He lacks the leadership strength at this point to turn against people who supported him, and he lacks the moral authority to say, ‘No, you can’t do that.’ ”

More fundamentally, making choices that would divide the governing alliance goes against Mr. Zuma’s instincts as an African traditionalist who seeks to settle conflicts by gathering his coalition under a metaphoric marula tree to talk for days or weeks until they reach a consensus, said Allister Sparks, a veteran commentator here. “Action dies in the process of eternal, everlasting debate,” Mr. Sparks said.