A top White House adviser on Sunday warned that the U.S. is facing Great Depression-era economic pain from the COVID-19 pandemic as major business leaders said there is essentially no chance of a substantial economic rebound before the fall.

The grim forecasts were announced as governors across the country increasingly allow a limited number of businesses to reopen. They say sufficient public health safeguards are in place and they need to get the stunted economy moving again.

“Make no mistake: It’s a really grave situation,” White House senior adviser Kevin Hassett said on ABC’s “This Week.”

“This is the biggest negative shock that our economy, I think, has ever seen,” said Mr. Hassett, a former chairman of the White House Council of Economic Advisers under President Trump. “We’re going to be looking at an unemployment rate that approaches rates that we saw during the Great Depression.”

More than 26 million Americans have filed unemployment claims over the past five weeks. That number amounts to roughly one-sixth of the U.S. workforce. The peak unemployment rate during the Great Depression was approximately 25%.

Treasury Secretary Steven T. Mnuchin, meanwhile, said Americans should see a substantial rebound in July, August and September after the economy starts to reopen in May and June.

“We are putting in [an] unprecedented amount of fiscal relief into the economy. You’re seeing trillions of dollars that’s making its way into the economy, and I think this is going to have a significant impact,” Mr. Mnuchin said on “Fox News Sunday.”

Congress cleared a nearly $500 billion relief package Friday, and the Small Business Administration is slated to start accepting more applications for a popular small business lending program Monday morning.

Mr. Mnuchin was asked about projections from the nonpartisan Congressional Budget Office showing that gross domestic product will shrink by 5.6% over the course of 2020 and that the unemployment rate will be close to 12% by the end of the year.

The secretary said the situation is unprecedented because the U.S. economy has essentially been closed down.

“So all these models are based upon health assumptions, how quickly we reopen, so we’ll see,” Mr. Mnuchin said. “As businesses begin to open, you’re going to see [the] demand side of the economy rebound.”

Major business leaders were skeptical of such a comparatively rosy scenario.

Barry Diller, chairman of IAC and Expedia, said there is no chance of a substantial rebound by the summer but there could be some positive movement by September.

“To anyone who thinks that this economy is going to bounce, I mean, you’d have to have the idea of a rubber ball not in existence to think it’s going to bounce high. It can’t,” Mr. Diller said on CBS’s “Face the Nation.” “The damage that’s being done is catastrophic.”

Bank of America CEO Brian Moynihan said on the same program that the U.S. economy is unlikely to return to pre-pandemic levels this year.

“This is a deep recession and then back out,” he said. “Our experts think it’s late next year when the economy gets back to the same size it was prior to this.”

Some governors are relaxing coronavirus-related restrictions in their states to allow a limited number of businesses to reopen.

Oklahoma Gov. Kevin Stitt, a Republican, said hospitalizations in his state peaked at 560 in late March and the numbers are now at about 300.

“I’ve been very clear with Oklahomans that coronavirus is still in the United States and it’s still in Oklahoma, so we have to continue with the social distancing. But we will start taking some measured reopening in a phased, measured approach,” Mr. Stitt said on “Fox News Sunday.”

Salons and barbershops were allowed to reopen in states including Oklahoma and Georgia starting Friday. Restaurants and other retail shops will follow soon.

“I’m giving guidance. If a restaurant doesn’t feel like they’re ready to reopen, they don’t have to,” said Mr. Stitt, noting that he has let mayors make their own local decisions.

Colorado Gov. Jared Polis, a Democrat who has announced a phased reopening in his state, acknowledged concerns about a potential second “spike” in COVID-19 cases as early as July.

“We have to make the best-informed decisions, based on data and science, with the information we have,” Mr. Polis said on CNN’s “State of the Union.” “We’re encouraging that every Coloradan who can works from home, and every business that doesn’t have to open right away waits a few weeks and takes their time, and making sure they do it in as safe a way as possible.”

More than 950,000 cases of COVID-19 and more than 50,000 related deaths have been reported in the U.S., according to a tracker from Johns Hopkins University.

President Trump singled out Georgia Gov. Brian Kemp, a Republican, last week. He said the governor was pressing forward too quickly with reopening plans.

Dr. Scott Gottlieb, a former head of the Food and Drug Administration under Mr. Trump, said Sunday that Georgia is “jumping the gun” and is “certainly not out of the woods.”

“They may have plateaued in their epidemic maybe, but they’re still accruing a lot of new cases and they certainly aren’t coming down in terms of the number of new cases each day,” Dr. Gottlieb said on CBS.

Under White House guidance, states are supposed to have sustained declines in documented coronavirus infections or positive tests before they start to gradually relax restrictions.

Dr. Deborah Birx, the U.S. coronavirus response coordinator, said she has had good conversations with governors who understand the risks and talk about reopening like turning up a “dimmer” rather than flipping an on/off light switch.

“We look at things in a very granular way, and governors should be doing the same,” she said on NBC’s “Meet the Press.”

Vice President Mike Pence has said the U.S. could largely get past the pandemic by Memorial Day.

But Dr. Birx said mitigation provisions, such as maintaining at least 6 feet of distance from others, should remain in place beyond that time frame.

“Social distancing will be with us through the summer to really ensure that we protect one another as we move through these phases,” Dr. Birx said.

She said the federal government and the states have made progress in expanding testing capacity.

“We have to have a breakthrough,” she said. “This RNA testing will carry us certainly through the spring and summer, but we need to have a huge technology breakthrough, and we’re working on that at the same time.”

More than 5.1 million tests for the coronavirus are estimated in the U.S., though some experts have called for the number of tests to hit roughly 3 million per week.

Dr. Anthony Fauci, a member of the White House coronavirus task force, said over the weekend that the U.S. is probably conducting 1.5 million to 2 million tests per week.

“We probably should get up to twice that as we get into the next several weeks, and I think we will,” said Dr. Fauci, director of the National Institute of Allergy and Infectious Diseases. “Testing is an important part, but it’s not the only part.”

Experts also agree that testing for antibodies, which could show the number of people who are immune to the virus, will also be key to the recovery.

The World Health Organization warned late last week that there is no evidence that recovered COVID-19 patients are immune from reinfection.

Dr. Birx said WHO was being “very cautious.”

“I think what WHO was saying, ‘We don’t know how long that effective antibody lasts,’” she said on CNN. “I think that is a question that we have to explore over the next few months and over the next few years. But I think everything that the WHO said should be happening, we’re doing here in the United States to help the American people.”

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