The rally last week at Manhattan's Riverside church was packed. Several thousand people crammed into the famous hall where Martin Luther King once gave a 1967 speech against the Vietnam war and for a fight against poverty.

The gathering was part of the Living Wage New York campaign, which aims to force companies who receive large grants of public money for private projects to pay workers in the jobs they create a minimum wage of around $10 (£6.47) an hour. It does not sound a controversial plan or one to create major unrest.

But the mood beneath the church's soaring vault was angry. Most of it was directed at one man, New York's billionaire mayor, Michael Bloomberg, who wants to veto the proposal.

Council member Jumaane Williams could not contain his fury. "This is about greed," he fumed to the crowd before turning his ire on Bloomberg and his vast fortune. "Ten dollars is not a lot of money! If Mayor Bloomberg woke up making 10 dollars an hour, he would faint!" he thundered, adding that the mayor ran New York like a "coward dictator".

Bloomberg, 69, who is now one of the most recognised names in American politics, is not usually the target of such strong emotion. He is often spoken of as a potential third party presidential candidate and ideal person to thread the needle of America's two-party set-up. He is hailed as a socially liberal moderate who is friendly to big business. He has, after all, been a member of both the Republicans and the Democrats.

But these are no ordinary times for Bloomberg. In the middle of economic hardship and financial crisis, sparked by a reckless banking industry, he has emerged as a staunch defender of Wall Street. While the Occupy Wall Street movement has spread from Manhattan around America, his administration has used the police to brutally crack down on demonstrators in New York – and the media covering them. He has defended the banking industry as patriotic and vital for New York's finances, despite polls showing deep anger with big finance. And he sees the Living Wage bid for a $10-an-hour pay packet as a reckless "job killer".

He has also become more prone to gaffes. New York police recently arrested a terror suspect, José Pimental, after officers assisted him in devising a fake bomb plot to attack the city. Bloomberg personally trumpeted the arrest of the so-called al-Qaida sympathiser. However, within hours the story's impact turned negative as it was revealed that the FBI refused to help with the case, believing Pimental was not a credible threat.

The controversies have all focused America's mind on the mayor of its most famous city as he contemplates the final two years of his last term in office. It has prompted a critical rethink in some quarters of just how Bloomberg has run New York and the legacy he will leave behind in a city that, always controversially, considers itself the unofficial capital of the world. And, just as the American political landscape seems ripe for a third-party run, it also appears that the man most usually associated with such a bid is making uncharacteristic mis-steps.

Perhaps that explains the New York Observer's front page last week. Under the headline "Digging In", the paper ran a huge cartoon of Bloomberg's head superimposed on a Thanksgiving turkey being served up to potential successors wielding knives and licking their lips.

It seems, in the eyes of New York media at least, that Bloomberg is suddenly vulnerable. That is remarkable for a man whose savvy political touch – and willingness to spend tens of millions of dollars of his own fortune on campaigns – made him untouchable as a politician. After all, Bloomberg's sheer chutzpah saw him change a term limits rule just so he could serve three times in office. Then, having won his third race, he supported a move back to two-term limits and closed the very loophole he had used himself.

If any one thing is currently tarnishing Bloomberg's record in office, it is his handling of the Occupy protests and his pro-banking industry stance. The police have used a heavy-handed approach to the growing protests that set up a world-famous encampment in downtown Manhattan's Zuccotti park.

There were pepper-spray incidents on female protesters, mass arrests on the Brooklyn bridge and a secretive early-morning raid to clear the park. That latter incident caused widespread protests from media organisations that were kept away from the site. Reporters were manhandled, beaten or arrested despite having press accreditation. In words that sparked ridicule on websites such as Twitter, Bloomberg said that the press had been kept away from the action for their own safety.

"There is a real hostility towards public expression in the street," said Professor Joshua Freeman, an expert on the city's history at the City University of New York. One Bloomberg watcher, who did not want to be named, was more blunt, saying that the police hard line was a manifestation of the mayor's personal attitude to the anti-capitalist protests: "I think this is him. It is what he is about."

There is little doubt that Bloomberg is a defender of America's brand of free market capitalism, even as the Occupy movement's cry of "We are 99%" has entered into political debate. Bloomberg, after all, founded the media company that bears his name, which has made him a vast fortune from financial news and data services.

"Mayor Bloomberg has become a spokesman for Wall Street. He comes off as a clear member of the 1%, defending the interests of the 1%," said Professor Bruce Berg, an expert on New York City politics at Fordham University.

However, Berg added: "But that is nothing citizens of New York didn't know from the outset."

Indeed, many experts say that Bloomberg's current travails are unlikely to impact his overall legacy. When his 12 years are up in 2014, he will still be seen as a highly competent, if autocratic, manager who made a dizzyingly complex city work well. "His administration has been exceptionally competent. New York runs better on a day-to-day basis than at any time I can remember," said Freeman.

Bloomberg has presided over rapid gentrification of many parts of the city, even as poorer residents are forced out. Many city streets have become safer and he has launched high-profile "green projects", such as planting hundreds of thousands of trees, building bike lanes and trying to push congestion charges.

He banned smoking and forced fast-food chains to post calorie counts on menus. Critics say that Bloomberg's New York has become a far more homogeneous, less diverse place that has lost the edge and rawness that made it famous. But that is probably not a criticism Bloomberg dislikes. Neither does everyone think it is fair. "The boom in real estate prices made it difficult for New York to be the way it was. A lot of that was out of Bloomberg's control," Freeman said.

But what will Bloomberg do next? At least one man is hoping the answer is to run for president in 2012. "He's the best person to create a needed third party in the United States," said Carey Campbell, national chairman of the Draft Michael Bloomberg Committee, which aims to pave a way for Bloomberg to join the presidential race. "He's a brilliant man, both in the private sector and as a mayor."

For his supporters, Bloomberg's appeal is based on free-market sympathies, coupled with social liberalism and a record at getting things done.

They also argue that his wealth makes him immune to "special interests" that are flooding American politics with much-needed campaign donations. Aside from Campbell's movement, Bloomberg could also get ballot access via Americans Elect, an online third-party movement that will choose a nominee by a popular vote in the summer. His name is already being touted as a possible pick for AE.

However, Bloomberg himself has publicly denied that he would run and most observers expect him to sit out the race. After he leaves office, he will remain a high-profile name with a fortune counted in billions and owner of one of the world's fastest-growing and most influential media companies.

Indeed, some might say, that is a more powerful position than simply holding elected office. He could influence debates, fund causes and still shape the world. On the left, George Soros has done just that. On the right, so have David and Charles Koch. Their billions give them power most politicians only dream of.

It might even be the one area where Bloomberg and the Occupy protesters finally agree on a basic truth: in modern America, money buys power and politics sometimes cannot.