“The apex is higher than we thought and the apex is sooner than we thought,” Mr Cuomo told reporters on Tuesday.
He said the federal government was not sending enough equipment to combat the crisis, noting the state needs 30,000 ventilators.
New York now has over 25,000 confirmed virus cases and at least 210 deaths.
“We need federal help and we need the federal help now,” Mr Cuomo said.
“New York is the canary in the coal mine, New York is happening first, what is happening to New York will happen to California and Illinois, it is just a matter of time.”
“I NEED 30,000 VENTILATORS”
The governor blasted the 400 ventilators sent to New York from the US Federal Emergency Management Agency (Fema).
“Four hundred ventilators? I need 30,000 ventilators. You want a pat on the back for sending 400 ventilators?… You’re missing the magnitude of the problem.”
New York currently has 7,000 ventilators, Mr Cuomo said.
The state is also looking into creating more healthcare space, possibly by turning dormitories and hotels into makeshift hospitals.
“You pick the 26,000 people who are going to die because you only sent 400 ventilators,” the governor added.
With 25,665 cases in New York, the state accounts for more than half of all US infections.
The number of new cases in the state is doubling every three days, the governor said, showing no signs of slowing down.
Mr Cuomo noted that the curve had not “flattened” in his state – meaning the rate of infections could overwhelm the healthcare system. New York may need up to 140,000 hospital beds in a worst-case scenario, he said.
The governor also criticised the notion that the economy needed to be saved, saying he would not “put a dollar amount on human life”.
“My mother is not expendable and your mother is not expendable.”
In a news conference on Monday, President Donald Trump had suggested the US would be “open for business” again soon, saying the US could not afford to “let the cure be worse than the problem”.
“We’re not willing to sacrifice that 1 or 2%,” Mr Cuomo emphasised.
“We are going to fight every way we can to save every life that we can because that’s what, I think, it means to be an American.”
What is the current US situation?
There are over 46,500 confirmed cases and nearly 600 deaths attributed to Covid-19 in the US. The World Health Organization on Tuesday said the US could become the next epicentre of the pandemic given the “very large acceleration in cases”.
States have been tightening lockdown measures despite Mr Trump signalling he was inclined to lessen restrictions soon.
On Tuesday, Wisconsin, Delaware and New Mexico enacted stay-at-home orders, bringing the total number of states issuing such policies to over a dozen and affecting about one in three Americans.
Lawmakers on Capitol Hill have been debating the details of an economic stimulus package that could total over $2tn (£1.7tn).
Democrats and the White House indicated negotiations could conclude on Tuesday, with Treasury Secretary Steve Mnuchin saying “the president wants us to get this done today”.