Top CEOs, in private conversations and pleas to President Trump, are warning of economic catastrophe if America doesn't begin planning for a phased return to work as soon as May, corporate leaders tell Axios.

Why it matters: The CEOs say massive numbers of companies, big and small, could go under if business and government don't start urgent talks about ways groups of workers can return.

Several of these leaders told us they want to have a hard national conversation about tradeoffs involved in any widespread lockdowns beyond the middle of next month.

They know most wouldn't return until June or later, but fear a lack of urgency on many going back sooner.

They realize it sounds callous to talk about work when people are scared of death, but believe it's an urgent debate the nation needs. Several are debating going public with this concern, but fear the optics and timing look discordant.

A return to work might start by geography, demography or type of work.

The plan likely would include guidelines about use of gloves and masks.

It would also err on the side of people who had the virus and healed, as well as those who pass instant antibody tests.

Reality check: Large parts of the South and central U.S. may not hit their peak until May.

Anthony Fauci said last week: "I think if we get to the part of the curve ... when it goes down to essentially no new cases, no deaths at a period of time, I think it makes sense that you’re going to have to relax social distancing."

Gary Cohn, the first White House economic adviser under Trump, told us that startup founders and CEOs are pleading privately: "We just need a realistic timeframe, and we need to talk honestly about it so we can tell our employees."

"There are a lot of conversations going on: At what point does a business become unrecoverable?" Cohn said.

"Business owners are asking: 'At what point do I just lay my people off and shut down and give the landlord the key?'"

"Businesses worry that their employees will be forced to jump at the first job offer, so they can't count on them to come back."

Mark Cuban, owner of the Dallas Mavericks, agreed it's a hot topic of private chats:

"A lot of people are concerned," he said Friday at an Axios virtual event.

But he said he'll "err on the side of safety, every single time."

Cohn, former president and COO of Goldman Sachs, said entrepreneurs and business titans also worry about the depression and addiction issues that have accompanied past economic downturns:

"No one wants to talk about this, but can you even get workers back who aren't so addicted or depressed they can actually function?"

What's next: Look for business groups to begin to broach these topics publicly in the next few weeks.

"If this goes on too long, the fear builds more and more," a top executive of a global company told us. "We need to lay the groundwork for the fear to ebb."

As Bloomberg put it, some investors are "willing to risk some horrors to avoid others."

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