The warnings from Cuomo and Pelosi came as the governor revealed that the number of coronavirus cases in New York is peaking sooner than expected. Trump and his top economic advisor, Larry Kudlow, both suggested Tuesday that the government would relax strict guidelines designed to slow the spread of the coronavirus.

Also Tuesday, House Speaker Nancy Pelosi , D-Calif., during an interview with MSNBC said, "The cost to the economy of many more people getting affected and sick is an even bigger cost than we're seeing now."

"But if you ask the American people to choose between public health and the economy then it's no contest. No American is going to say 'accelerate the economy at the cost of human life,'" Cuomo argued.

"I understand what the president is saying that this is unsustainable that we close down the economy and we continue to spend money. There is no doubt about that," Cuomo said at a news conference in New York City.

Cuomo warned, as many health experts have, that many more people could die than otherwise would if there is a pullback in widespread efforts to slow the spread of the virus.

New York Gov. Andrew Cuomo on Tuesday pushed back hard against the idea raised by President Donald Trump of easing restrictions from coronavirus mitigation efforts in an effort to revive the U.S. economy.

Trump said Tuesday, "I would love to have the country opened up, and just raring to go, by Easter," which is on April 12 this year.

Health experts have said that slowing the rate of transmission is essential to avoid overwhelming the capacity of hospitals to treat critically ill patients with the coronavirus.

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The now widely used phrased "flatten the curve" refers to keeping the peak level of current coronavirus cases below the level of available beds in intensive care units. Experts say steps like closing nonessential businesses, schools and limiting contacts between people are crucial to accomplish that goal.

An analysis by researchers at Imperial College in London projected that 2.2 million Americans could die from COVID-19, the disease caused by the coronavirus, without suppression efforts like the ones adopted by states and encouraged by the federal government.

With restrictions, the death toll could drop to 1.1 million, or less, depending on the strength and prevalence of restrictions.

But in recent days, Trump has chafed at the dramatic economic fallout of those restrictions, which have rocked stock market indexes, and threatened to leave the U.S. in recession when he stands for reelection in November. On Tuesday, he repeated a warning that "the cure cannot be worse ... than the problem."

Trump tweeted Tuesday: "Our people want to return to work."

"They will practice Social Distancing and all else, and Seniors will be watched over protectively & lovingly. We can do two things together," Trump tweeted. "THE CURE CANNOT BE WORSE (by far) THAN THE PROBLEM! Congress MUST ACT NOW. We will come back strong!"

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Kudlow, director of the National Economic Council, said later Tuesday morning that some states with low numbers of confirmed cases might be able to ease off their restrictions quickly.

Dr. Scott Gottlieb, who served in the Trump administration as director of the Food and Drug Administration, warned Monday night on Twitter that, "There's a strong and understandable desire to return to better times and a functioning economy."

"But it should not be lost on anyone that there's no such thing as a functioning economy and society so long as covid-19 continues to spread uncontrolled in our biggest cities," wrote Gottlieb, who is a CNBC contributor.

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Gottlieb told CNBC's "Squawk Box" on Tuesday: "This is going to be a long fight" to slow the spread of the virus.

"I think we need to keep this going a couple of more weeks," he said.

"It's going to be another three, four weeks until we see the peak of the pandemic curve," Gottlieb said.

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Richard Horton, editor-in-chief of The Lancet, a British medical journal, blasted Trump's idea of easing guidance on the coronavirus.

"President Trump: you once called COVID-19 'the new hoax' and now you say 'we're not going to let the cure be worse than the problem,'" Horton wrote.

"You are facing a virus that will kill thousands of Americans unless you suppress transmission and shield the most vulnerable. Step up."

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Neil Ferguson, lead author of the Imperial College analysis, has said on Twitter in recent days that "the first priority is to get case numbers down."

"There will then be a (limited) breathing space to assess less disruptive longer term solutions," Ferguson wrote.

An Atlantic article published Monday noted that coronavirus mitigation "actions take a massive economic toll: millions of lost jobs, billions if not trillions of dollars of wealth wiped away."

"It is tempting, at this point, to say that the cure is worse than the disease," wrote the authors, Dr. Aaron Carroll, professor of pediatrics at Indiana University School of Medicine, and Dr. Ashish Jha, professor of Global Health at Harvard University.

"It isn't. While the cure has large side effects, the disease is worse. The real problem is that we're taking our medicine haphazardly—and as a result, experiencing all of the side effects and few of the benefits. That needs to change."

The authors called for "a true national pause — a cessation of all nonessential activities" for at least two weeks, with total participation by U.S. residents.

"If we all distanced ourselves from one another for that long, the outbreak would slow down significantly," they wrote.

The article also said it was essential to have "massive, coordinated testing of the population."

"Even today, we don't know how many people are infected in the community and how many people without symptoms are spreading the infection to others."