Seven inches of snow dumped over New York on his second day in office is not the only blizzard Bill De Blasio, the newly instated mayor, is having to negotiate. He is also heading into a political blizzard over his plans to tackle inequality by raising taxes on the very rich.

The 109th mayor used his inaugural speech on 1 January to issue a liberal clarion call of the type not heard in New York – or arguably anywhere else in the US – for at least 20 years. As the first Democratic mayor to take office in the city since 1994, he vowed to take on what he has dubbed "the Tale of Two Cities" – the vast income gap that sets a sparkling and buoyant Manhattan apart from the grinding poverty found in the outer boroughs.

The pledge pits De Blasio, a towering 6ft 5in presence armed with an overwhelming electoral mandate from 73% of New Yorkers, against the city's fiscally conservative establishment as well as the political leadership of Albany, the state capital, which holds sway over tax rates. How he emerges from what promises to be a bruising fight could determine the fate of his new mayoralty – and affect political debate across America.

"Bill De Blasio is strikingly out of step with the political agenda of New York for the past two decades – this is back to the future stuff," said Columbia university professor William Eimicke, who has held several positions in New York government.

Eimicke puts De Blasio's chances of getting his tax plan through Albany at "slim to none". The legislature and state governor Andrew Cuomo both face re-election in November and, as Eimicke points out, a disproportionate percentage of their campaign funds are donated by New York City's nearly 400,000 millionaires.

Yet De Blasio, 52, is pushing his plan with the assertiveness of a politician who feels the force of history, fuelled by welling anger among low- to middle-income Americans about the perceived injustice of a system that benefits "the 1%". In his speech, he ridiculed those who believe "that the way to move forward is to give more to the most fortunate". Instead his administration would focus on the "inequality crisis" facing a city in which the top 1% earns 39% of all income.

To confront the crisis, the new mayor has proposed a package of radical policies, including affordable housing quotas for big developers and extending paid sick leave to 30,000 additional New Yorkers. But the most controversial element is to extract an extra $530m (£323m) in taxes from those earning more than $500,000 a year to pay for universal pre-kindergarten education and after-school programmes.

Anyone taking home up to $1m annually would have to pay $973 a year on average in increased taxes. "That's less than three bucks a day – about the cost of a small soy latte at your local Starbucks," De Blasio quipped.

Response to De Blasio's battlecry has so far been muted in the wake of his inaugural address. "I sense that a lot of people are pretty nervous about what the next few years are going to bring, but folk at the top are in a wait-and-see mode as they try to figure out whether the new mayor is prepared to work with them," said Scott Winship, a senior fellow at the conservative thinktank the Manhattan Institute.

Critics of the tax plan were less restrained before De Blasio's inauguration, judging from views assembled by Bloomberg News. Hedge fund manager EE "Buzzy" Geduld said it was the "most absurd thing I've ever heard", while investment banker Peter Solomon said that De Blasio was "barking up the wrong tree". Michael Bloomberg, De Blasio's billionaire predecesso r, who presided over the growing income gap during his 12 years as mayor, denounced the plan as "unfair" and said it would drive the rich out of the city. "Places like London are going to eat our lunch," he said.

On the other side of the battle stand figures such as progressive billionaire George Soros, who has called the plan "sound public policy", and actors Steve Buscemi and former Sex and the City star Cynthia Nixon, who both attended De Blasio's inauguration.

The individual to watch in the pending storm is Cuomo, who has the power to veto any tax increase even should the legislature vote for it. He has promised to cut state tax rates in his own bid for re-election, and has so far been careful to keep his distance from De Blasio's progressive fiscal ideas. But the two men are friends – De Blasio used to work for Cuomo in Bill Clinton's administration. Cuomo also has presidential ambitions and, as a savvy politician, knows when to bend with the prevailing wind.

"The media is going to play a key role here," said Eimicke. "If Sixty Minutes and the news outlets portray this as a new wave in American politics, and De Blasio as a courageous man taking on inequality, they could create an oomph that will make other politicians afraid to oppose him."