The wealthiest 1 percent of New Yorkers control about 31 percent of the state’s income, according to data from the Economic Policy Institute, a Washington-based think tank. They also account for half of the state’s income taxes, according to Mr. Cuomo.

“There is a tipping point where people say, ‘I love New York, but to spend another $300,000 in taxes, I’ll move to Florida,’” the governor, a Democrat, said in a radio interview last week. “You know, tax the rich, tax the rich, tax the rich. Most progressive tax code, proud of it. But now look at how fragile your economy is.”

The State Senate’s Democratic majority leader, Andrea Stewart-Cousins, of Westchester, has also dismissed the idea of new taxes.

Of course, progressive activists have argued for years that higher taxes on the rich would not hurt the state’s economy. But the Patriotic Millionaires’ hope — and that of the grass-roots groups aligned with them — was that the message would have more weight coming from, well, the rich.

“New York will always be New York. There’s no other place like it, and millionaires are concentrated here because of that,” said Abigail Disney, the great-niece of Walt Disney and a member of the Patriotic Millionaires.

The state’s current tax on high earners, which was branded as a millionaire’s tax but affected people earning more than $300,000, was introduced in 2009.

Between then and 2016, the number of millionaires filing taxes in New York increased by 72 percent, with those millionaires’ total income increasing by 54 percent in that time, according to the Fiscal Policy Institute, a union-backed nonpartisan think tank. Non-millionaires’ income increased by 33 percent in the same period.