The overwhelming support of New York City voters for Bill de Blasio is the latest sign of the shift towards a new populist left in America. De Blasio owes his unexpected tailwind to campaigning on issues considered by insiders to be too polarizing for winning politics.

One is De Blasio's promise to redress the "tale of two cities" inequalities among New Yorkers, an issue forced into mainstream discourse by the 2011 Occupy Wall Street movement – not by New York Democrats aligned with Wall Street. The other is De Blasio's pledge to sharply curb police stop-and-frisk policies directed against young people of color – aggressive tactics favored by a majority of white voters and overwhelmingly criticized by African Americans, Latinos and Asian-American voters.

Despite its Democratic voter majority, New York in recent decades has been the political stronghold of the plutocratic Mayor Michael Bloomberg and, before him, the abrasive law-and-order Mayor Rudolph Giuliani – both Republicans with national, even global, reach. Democrats have lacked a progressive voice on the national stage of American politics often provided by the New York mayor's office – until now.

De Blasio will have a mandate for economic and social reform backed by a newly-elected 51-member city council, the most progressive in years. As Juan Gonzáles of Pacifica's DemocracyNow! put it:

I can't think of a time like this when so many progressives have been elected at once.

With American politics polarized between the Obama center and the thriving Tea Party, the only opening for the left is through state and local federalism serving as "laboratories of reform", to paraphrase former Justice Louis Brandeis. After the Gilded Age and the Great Crash of the 1920s, New York Mayor Fiorello LaGuardia (1934-47) and legislators like Robert Wagner created the first pillars of the New Deal before it become the national platform of the Democrats. They successfully fought not only Wall Street bankers, but a virulent and racist American right.

De Blasio is positioned to similarly shift the nation's dialogue, policies and priorities in a progressive direction – assuming he delivers on his campaign pledges. Since the financial crisis of 2008, the federal government has passed a loophole-ridden Dodd-Frank reform law, which failed even to regulate the trillions floating in the derivatives industry. Wall Street investors have been richly rewarded since then, while middle-class incomes stagnate and the numbers of poor Americans reach the highest in 50 years. A report last week from the respected American Community Survey noted:

No other major American city has such income inequality when it comes to rich and poor when it comes to New York.

Among De Blasio's first challenges will be prodding Governor Andrew Cuomo and the state legislature in Albany to permit local tax increases to fund universal pre-kindergarten in New York City. Cuomo and most pundits say the De Blasio proposal is going nowhere, but seasoned reporters like Gonzales are not so sure. "It's hard but doable. I'm not sure that Albany will resist the home rule message from a new mayor with a large mandate."

De Blasio has direct power over New York City's $70bn budget and re-zoning policies, which, under Bloomberg, showered favors on a real estate industry bent on competing with London and Hong Kong at the expense of residential neighborhoods. An early test for De Blasio will be the Midtown East re-zoning project left unfinished by Bloomberg, which would erect Empire State Building skyscrapers from the East River to downtown. De Blasio wants to "fix" the proposal, while community groups are 100% opposed, saying they would be left in permanent shadows.

De Blasio also can tackle income inequality by signing the living wage ordinance on city contracts, or by preventing Wall Street developers getting special city abatements – measures that Bloomberg vetoed. De Blasio didn't flinch on the issue when confronted in closed meetings with developers during the campaign.

When De Blasio first raised his opposition to the police stop-and-frisk policies, according to Vincent Warren of the Center for Constitutional Rights, the candidate began rising in the polls against other contenders in the Democratic primary. The stop-and-frisk policy, a variation of racial profiling against black and brown young people, is generally supported by white and worried New Yorkers and overwhelmingly opposed by communities of color.

De Blasio and his African-American wife have a teenager, named Dante, whose Afro style even caught the attention of President Obama. As Dante leafleted with his father at subway turnstiles, emotional memories of the murdered Florida teenager Trayvon Martin were palpable, if rarely mentioned.

New York under Mayor Giuliani fanned then popular American policies of mass incarceration towards youngsters who resembled Dante de Blasio. From 2008 to 2012, the NYPD stopped nearly 2.9 million New Yorkers, a majority of them young, about 85% black or brown. On average, 88% of those stopped were completely innocent of any crime or misdemeanor.

When a federal appeals court halted a judicial order ordering detailed changes in the NYPD last week, De Blasio expressed "extreme disappointment" and pledged to move forward on police reform from day one. How he will do so is procedurally muddled for the moment, but there is little doubt that another staple of the Bloomberg era is ready for the dustbin.

Will De Blasio adhere to his promises? He is, after all, a mainstream Democratic party operative and policy wonk who once managed Hillary Clinton's centrist campaign for the US Senate. Decades ago, he was deeply involved in the Nicaragua Solidarity Movement against Ronald Reagan's illegal contra war. De Blasio seemed nervous when this past association surfaced earlier in the campaign. But the Republicans could gain no traction on the issue.

It is reassuring that De Blasio has roots in past social movements instead of the usual pedigrees for a political career. If he has veered back to his lefty roots, it is enabled by a popular anger among voters. This anger was fanned by the growing gap between the haves and have-nots, reinforced by heavy-handed policing, in a city whose power brokers are addicted to opulence.

The media widely acknowledges that Occupy Wall Street "changed the conversation" in America. De Blasio won't represent the 99%, but a healthy majority will do. From Wednesday, Bill de Blasio will have the largest megaphone of any conversation-changer on the national scene.