Since coming into office, Trump has wielded federal power against several Democratic-run cities, sending national guard troops and cracking down on immigration across the US.

He has also cut billions of funding to cities since the government shut down on 1 October, including New York, where he froze $18bn (£13.6bn) in federal money for major infrastructure projects.

Political experts told the BBC Trump could easily slash more - and that could hamper Mamdani's campaign promises to reduce the cost of living.

The self-described democratic socialist had campaigned for free and faster buses, rent freezes for rent-stabilised housing, universal child care and city-run grocery stores, among other policy goals.

"The reality is the mayor-elect will have to focus a lot of his attention on President Trump and the attacks on New York, as opposed to all the issues he wants to deal with," said Julian Zelizer, a professor of history at Princeton University. "It will be a problem for the city and it will also be a problem and a challenge for the mayor-elect to stay focused."

Mamdani did not respond to a request for comment from the BBC.

Mamdani, a former state assemblyman, faces several challenges aside from Trump in accomplishing his ambitious policy goals, policy experts say.

He has suggested he could raise $10bn in revenue by increasing taxes for wealthy corporations and the top one percent of earners in New York - but that would require approval from the state's governor.

Democratic Governor Kathy Hochul, who is facing a tough re-election bid next year, has so far been hesitant to support Mamdani's tax plan. Trump ally Elise Stefanik has said she will seek the Republican nomination for the state's top job.

Trump could poke further holes in these plans if he cuts more federal funds, which last year comprised about $8.5bn, or 7% of the city's total budget.

"There is going to be a money issue to do anything in the city," Mr Zelizer said. "But if federal dollars start to deplete, that makes it much harder to do anything new."

Those funds are used for a host of services, including the housing department, emergency response to disasters, and children's services, as well as education funds for lower-income students and school meals, according to the New York City Independent Budget Office.

Trump has not specified which federal funds he would target.

New York is legally required to provide some of these services, such as funding for homeless shelters. That means that without federal funding, the city and state government would have to make up the difference, putting pressure on other programmes, said Sarah Parker, a senior research and strategy officer with the New York City Independent Budget Office.

"There are a lot of contingency plans being drawn at the city and state level for a whole lot of scenarios," she said.

Trump would likely face legal challenges for withholding funds that have been approved by Congress, which include food aid, said Justin de Benedictis-Kessner, a public policy professor at Harvard University's Kennedy School of Government.

"But it does slow down the process of getting those funds to the people who need them," he said.

Trump has also used the threat of law enforcement against Democratic-led cities. He has deployed National Guard troops across the country including in Los Angeles, Portland, Oregon and Washington DC, framing the cities as crime-ridden places that need federal intervention.

He has so far refrained from sending the troops to the largest US city, but political experts said that could change.

"He already has the template," Mr Zelizer said. "It's hard to imagine that doesn't happen."

Mamdani has said he would turn to legal challenges to respond to a National Guard deployment in New York, as other states have. Many of the cases are still in limbo, and working their way through the courts.

Political experts also expect Trump to expand his immigration crackdown in New York, which has been a sanctuary city since the 1980s. That means the city limits co-operation with federal immigration authorities.

The administration has already ramped up enforcement in the city's immigration courts, where US Immigration and Customs Enforcement (ICE) agents have arrested hundreds of people arriving for mandatory immigration hearings.

Current Mayor Eric Adams has mostly co-operated with the administration. But Mamdani - who came to the US from Uganda when he was seven - signalled a different course.

He said New York would "remain a city of immigrants, a city built by immigrants, powered by immigrants, and as of tonight, led by an immigrant".

"So, hear me, President Trump, when I say this: To get to any of us, you will have to get through all of us," he said on election night.

Adams did so after Trump's Department of Justice dismissed federal bribery and fraud charges against him. The move led to the resignation of the top New York prosecutor, who claimed Adams' lawyers had asked justice department officials to drop the case in exchange for enforcing Trump's immigration policies.

Mamdani will likely take time to craft a strategy for responding to Trump's first moves, as he won't take office until January, said Bob Shapiro, a political science professor at Columbia University.

Other Democratic city leaders have taken a variety of approaches, including progressive Boston Mayor Michelle Wu, who has frequently pushed back against the president. Trump once threatened to pull the World Cup games from her Massachusetts city.

In San Francisco, Mayor Daniel Lurie reportedly relied on technology industry leaders to dissuade Trump from sending National Guard troops to the city, arguing it would affect the economy.

Mamdani could make similar moves in New York to avoid federal troops, calling on Wall Street leaders from a city where Trump made his career in real estate, Mr Shapiro said.

In a policy document on "Trump-proofing" New York City, the mayor-elect said he planned to hire an additional 200 lawyers to beef up the city's legal department to respond to the Trump administration's "Presidential excess".

Mamdani faces big challenges in trying to implement his ambitious policy agenda, so he may pick and choose his battles with the president to build support among anti-Trump New Yorkers for certain policies, said de Benedictis-Kessner.

"I think he'll engage with Trump if that helps him accomplish his policy goals," he said. "And I think that he's a smart enough politician that he won't do that unless it does."