In recent weeks, Mayor Michael R. Bloomberg has been mocked as a Manhattan elitist on “Saturday Night Live,” booed for his educational policies and accused of ignoring far-flung corners of New York City paralyzed by snow.

But Mr. Bloomberg will take one step toward rebuilding a strained relationship with the city’s other boroughs on Wednesday when he announces a plan to make it easier for New Yorkers to hail a cab outside of Manhattan. The mayor’s proposal, part of his 10th State of the City address, would make it legal to hail livery cabs.

The speech, at 1 p.m. on Staten Island, will offer him an opportunity to reassert his agenda after a series of setbacks. He has endured a bruising battle over his new schools chancellor, an $80 million fraud scheme involving the city’s payroll system and a botched effort by the city to deal with a crippling snowstorm last month.

On Wednesday, Mr. Bloomberg will try to remind New Yorkers of his signature accomplishments, particularly his efforts to stimulate the economy. He is also expected to push for changes to the city’s pension system.

But looming over the occasion will be Mr. Bloomberg’s recent troubles, which have prompted talk that a third-term “curse” has claimed another mayor and that unpredictable problems may have tarnished his record.

Mr. Bloomberg has said he has no regrets about his having sought a third term. “I hope it was the right move for the city,” he said recently, “and I think it was the right move for me.”

It is far too early to offer a verdict on the mayor’s twilight term, but historians point to signs of trouble. “People can reasonably speculate that a more engaged and focused mayor would have handled things differently,” said Chris McNickle, a historian who has written about the city’s mayors. “It’s an office that tends to wear its occupants out.”

Mr. Bloomberg’s aides dispute the idea that he has lost focus or become less effective. “Look at the job creation we’ve had, look at the record on the budget, look at the fact that we’ve had less than 600 murders,” said Howard Wolfson, a deputy mayor. “If you look at the totality of the last 12 months, it is a powerful record.”

But not everything has gone smoothly. The mayor was heavily criticized for his choice of Cathleen P. Black, a former publishing executive with no educational credentials, as the city’s public schools chancellor. The anger over Ms. Black’s appointment and the highly secretive process that led to it has persisted: critics of Mr. Bloomberg’s educational agenda booed him on Monday at a Martin Luther King’s Birthday forum in Harlem.

Even before he decided to run for a third term, Mr. Bloomberg’s advisers warned him of the potential peril: Four more years would increase the risk of something unforeseen happening.

The blizzard last month epitomized those concerns. A Marist poll this month showed the mayor’s approval rating at 37 percent, the lowest since he took office.

The frustration among New Yorkers, analysts say, partly reflects pent-up anger over Mr. Bloomberg’s successful effort to rewrite city law so he could run for a third term, which many saw as undemocratic and arrogant. That anger largely dissipated as the mayor kept city government running smoothly.

But the perception that Mr. Bloomberg is acting out of self-interest has returned, Mr. McNickle said, reinforced by his forays into national politics. “People had given him a certain opportunity to re-earn the trust,” he said. “But in that context, the flirtations with national office are not helpful.”

In recent months, Mr. Bloomberg has lent his voice to an independent political group known as No Labels, and his media company, Bloomberg L.P., has announced plans to publish editorials that reflect his views.

The timing of the blizzard was especially inopportune for him. In the weeks before, the mayor had capped a season of political endorsements that took him from California to Rhode Island; he had delivered a high-profile rebuke of the government’s handling of the economic recovery; and he had traveled to Washington to be on “Meet the Press.”

Then the snow fell, and Mr. Bloomberg — for all his finger-wagging at others — seemed unable to get one of the most basic of municipal tasks accomplished.

As the scrutiny has increased, Mr. Bloomberg, known for his brassy rebuttals, has shown humility. He initially scoffed at suggestions that Ms. Black was not qualified, but reached a compromise that satisfied state officials.

Similarly, he was at first defensive of the city’s response to the blizzard. But after the shortcomings became apparent, he was quick to denounce the city’s response as inadequate.

Mr. Bloomberg’s supporters say the mayor must persuade New Yorkers that he can evolve.

The City Council speaker, Christine C. Quinn, said, “The question now is: Is he changing things to make sure he is learning from the mistakes?”

Former Mayor Edward I. Koch, whose own third term was bruised by scandal, said Mr. Bloomberg needed to continue to speak frankly about his missteps.

“The people of the city of New York are very generous,” Mr. Koch said. “All they want you to do is admit error.”

(Source: NY Times)