Representative Alexandria Ocasio-Cortez has joined a new campaign to push Gov. Andrew M. Cuomo to tax billionaires who live in New York State and use the money to assist people hurt by the pandemic-fueled economic crisis.

Similar measures targeting the wealthy have stalled in Albany, opposed by Republicans who long controlled the State Senate or by Mr. Cuomo, a third-term Democrat who has made his tax-cutting ways a central platform of his decade-long tenure.

But the environment has changed: Democrats gained control of both houses of the Legislature in a “blue wave” election in 2018, and the effects of the coronavirus-forced shutdown have created a $13 billion state budget shortfall.

Jessica Ramos, a state senator from Queens who was among the progressive Democrats who won office in 2018, sponsored the bill that would tax the unrealized capital gains of the state’s 119 billionaires. The money raised would be redirected to workers not eligible for unemployment insurance or the federal stimulus.

The proposed legislation is one of at least three tax-the-rich bills, including one that would impose an ultra-millionaires’ tax, that will greet the State Legislature when it returns for a rare July session on Monday.

But even with Democrats in control in Albany, the measures are still sure to encounter opposition from Republicans and many business leaders.

Mr. Cuomo has argued that taxes that target high earners could drive them out of the state and further damage the tax base — a concern that the governor’s budget director, Robert Mujica, underscored in an interview on Wednesday.

New York already has one of the highest tax rates for the wealthy in the country, Mr. Mujica said, adding that the top 2 percent of taxpayers already pay half of the state’s tax liability. The only effective way to get billionaires to pay more, he said, would be if Congress enacted a wealth tax on high earners.

“It’s interesting when you have people elected to Congress pushing for state action when they can’t get action in Congress,” Mr. Mujica said. “It’s absolutely necessary for the federal government to step up and provide the support we need.”

Ms. Ocasio-Cortez is part of a coordinated effort that aims to persuade Mr. Cuomo that the state should act first.

On Thursday, a campaign-like video was released that featured Ms. Ocasio-Cortez; Ms. Ramos; the New York City public advocate, Jumaane Williams; and two Assembly members, Carmen De La Rosa and Yuh-Line Niou.

“Governor Cuomo, we need you to pass a billionaires’ tax, in order to make sure that we’re providing for our working families,” Ms. Ocasio-Cortez said in the video. “It’s time to stop protecting billionaires, and it’s time to start working for working families.”

Also on Thursday, 100 immigrant workers started a 24-hour fast and sleep-out near the Fifth Avenue penthouse of Jeff Bezos, the founder of Amazon and one of the richest men in the world. On Friday, hundreds of people are expected to hold a “march on billionaires” that will end at Mr. Cuomo’s Manhattan office.

“We are calling for a just recovery for all New Yorkers, but right now our system is rigged to protect the mega-rich,” said Angeles Solis, lead organizer for Make the Road New York, one of the groups in the coalition.

Last year, a so-called pied-à-terre tax on the second homes of the wealthy in New York City gained some momentum after Kenneth C. Griffin, a hedge fund billionaire with an estimated net worth of $10 billion, purchased the most expensive single family home in the United States, a $238 million apartment on Central Park South.

Mr. Cuomo voiced support for the plan before it fell apart after the real estate industry exerted pressure on legislators.

But the financial crisis created by the coronavirus — the state estimates it needs more than $10 billion to stave off major cuts in education, health care and public safety — has forced lawmakers to reconsider implementing new taxes.

Last month, 103 Democratic legislators — including a majority in the State Senate — signed on to a letter that called for the wealthy to pay their share, and pledged not to allow budget cuts “without raising revenue from those who can most afford to pay more.”

Ms. Ramos, who represents areas of Queens hit hardest by the coronavirus, said the environment has changed since the failure of the pied-à-terre tax.

“The pandemic has only exacerbated the holes that already existed in our safety net,” she said. “It is much easier to make the case for taxing billionaires now that there is such widespread strife, and unemployment has never been higher.”

Ms. Ocasio-Cortez said that Ms. Ramos’s bill would give “much deserved economic relief” to the many people suffering from the effects of the outbreak, especially undocumented immigrants “who have been at the forefront of the crisis as essential workers.”

This is not the first time that Ms. Ocasio-Cortez, a Democrat who represents parts of Queens and the Bronx, has challenged the governor; she has criticized Mr. Cuomo over his plan to add more police officers to the subway.

Mr. Cuomo, in turn, has sought to diminish Ms. Ocasio Cortez’s role in scuttling the plans of Amazon to locate one of its headquarters in Queens. More recently, the governor said Ms. Ocasio-Cortez was mistaken in speculating that crime had risen because people were unable to pay their rent and were fearful of eviction; he pointed out that there was a state moratorium on evictions.

With Republicans no longer in charge of the State Senate, the proposals for new taxes on the wealthy will undoubtedly have a far greater chance of passing. But Robert G. Ortt, the Senate Republican minority leader, still asserted that a billionaires’ tax would be a mistake that would “send individuals who already pay for most of New York’s services away to lower tax states along with their businesses and jobs.”

“We need to examine spending and start cutting waste before everyone escapes from New York,” he added.

Yet in the end, Mr. Cuomo may be the biggest barrier to new taxes on the wealthy; the governor has insisted that the federal government must “step up” to help New York.

In late May, shortly after ringing the bell to reopen the New York Stock Exchange, the governor demurred when asked whether he’d support taxing the rich, saying he was “still banking on Washington doing the intelligent thing.”

“I still don’t want to create the possibility or the excuse for Washington to say, ‘Well, we don’t have to act,’” he said.

A recent analysis by Americans for Tax Fairness found that the wealth of New York’s 119 billionaires increased by $77 billion from March to June, a period that saw the state gain a new billionaire. The total net worth of New York’s billionaires grew to $600.7 billion from $521.5 billion from March to June, according to an analysis of data from Forbes.

“You are barely slowing down their growth in wealth,” said Frank Clemente, the executive director of Americans for Tax Fairness. “The pandemic has been fabulous for helping people understand how vulnerable so many millions of Americans are, and just how upside down the economic system is.”