New York (CNN Business) Wall Street has experienced a breathtaking rebound from the coronavirus crisis lows -- one that reflects a belief among investors that the US economy will enjoy a swift recovery from this historic collapse.

The S&P 500 spiked a stunning 27% between March 23 and Tuesday. It was the biggest 15-day rally in 87 years, according to Bespoke Investment Group. The Dow skyrocketed even further, gaining 5,300 points, or 29%, in that span.

The recent rebound was driven by relief over the emergency actions taken by Washington to avoid a full-blown financial crisis, or even a depression. Investors are encouraged by signs that the coronavirus may be at or near a peak, potentially allowing businesses to re-open next month.

The next challenge for the market is when reality hits that while we're past the worst of the virus, the process of reopening and the growth rate will still be really slow for a while.

Yet that optimism is not backed up by the reality on the ground. Health experts are warning of a potential second wave of infections that could lengthen the time social distancing remains in place. That's why many economists are not anticipating a speedy rebound.

Rather, they see a choppy recovery, marred by fits and starts.

"This will be anything but a V-shaped recovery," Mark Zandi, chief economist at Moody's Analytics, told CNN Business. "We'll get out of the gates fast when businesses start to open. But we'll be right in the quicksand because everyone will have an eye on the second wave."

Some of that concern is creeping into markets . The Dow dropped 445 points, or 1.9%, on Wednesday following a series of horrific economic releases.

'Long, hard road'

That's on top of the 16.8 million people who have filed initial unemployment claims during the crisis, a number that is expected to jump higher still when jobless claims for the latest week are released Thursday.

Economists at JPMorgan Chase estimate GDP will collapse by 40% during the second quarter, driving up the unemployment rate to 20%.

Some Federal Reserve officials are warning the economy could stay weak.

"This could be a long, hard road that we have ahead of us until we get to either an effective therapy or a vaccine," Minneapolis Fed President Neel Kashkari told CBS on Sunday. "It's hard for me to see a V-shaped recovery under that scenario."

San Francisco Fed President Mary Daly expects "something more, like negative quarters of growth throughout 2020, and then a gradual return to positive growth in 2021," she told The Wall Street Journal on Tuesday.

The great debate: Is the worst over for stocks?

Yet the stock market is still anticipating a more rapid recovery, setting the stage for a potentially painful disappointment.

"The next challenge for the market is when reality hits that while we're past the worst of the virus, the process of reopening and the growth rate will still be really slow for a while," said Peter Boockvar, chief investment officer at Bleakley Advisory Group.

That reckoning could eventually cause US stocks to retest those March 23 lows.

"We saw A bottom, but I don't believe it was THE bottom," said Boockvar.

This wouldn't be the first time there were multiple plateaus on the way to a market bottom. During the Great Recession, US stocks enjoyed multiple rebounds in late 2008 that raised hopes the worst was over. Yet the market didn't truly bottom until March 2009.

"I'm reluctant to say we've seen the worst," said Gus Faucher, chief economist at PNC Financial. "It's plausible we see stock prices move dramatically lower in the near term."

Others are more optimistic, especially because extremely low interest rates make risky stocks look much more attractive than bonds.

"Even though the market might get scared again, I don't think stocks are too high," said David Kelly, chief global strategist at JPMorgan Asset Management. "If you believe 2021 will be the first year of the rebound, then there are still good reasons not to be overly negative on stocks."

Fed chief: 'We need to make them whole'

Congress and the White House enacted a record-breaking $2 trillion stimulus package that provides relief to consumers and aims to keep small businesses alive. The Fed has rolled out trillions of dollars of lending facilities to keep credit, the lifeblood of the economy, flowing to households and businesses.

The fact that this crisis was caused by a virus, not greed, has freed policymakers to take an even more aggressive response.

"People are undertaking these sacrifices for the common good. We need to make them whole," Fed chief Jerome Powell said during a webinar last week with Brookings Institution . "They didn't cause this. Their business isn't closed because of anything they did wrong."

Marko Kolanovic, global asset strategist at JPMorgan, said those comments underscore his team's belief that stocks will reach record highs next year, likely by the first half of the year.

"Unhindered by moral hazard, the response of fiscal and monetary authorities is and will continue to be unprecedented," Kolanovic wrote to clients this week, "with the goal of essentially making everyone 'whole.'"

Yet it may not be realistic to think the government can eliminate all economic pain, especially if the health crisis lasts longer than anticipated.

"There will be a lot of small business failures," said Zandi of Moody's, adding that many very small firms may not have the resources to take advantage of the government's forgivable loan program.

"What lawmakers and the Fed are doing is critical to ensure we don't go into a complete blackhole," said Zandi. "But that doesn't mean they will forestall a lot of darkness. That's dead ahead."

The risk of a second wave

Health experts have warned the coronavirus pandemic could return later this year.

"If you mean it goes way down and then come September, October, November, we have another peak -- I have to say I would not be surprised," Anthony Fauci, the nation's top infectious disease expert, told the Associated Press on Tuesday.

That's why while the White House is seeking to reopen the economy as soon as May 1, many governors are reluctant to move that quickly. And new research suggests stay-at-home orders will stay in effect longer than anticipated.

The worry is that the United States reopens the economy too quickly, setting off another spike of infections -- which is already happening overseas.

"Asia is starting to see a second wave of infections, with Japan and Singapore both entering an exponential phase of growth in new cases," Matthew Harrison, biotech analyst at Morgan Stanley, wrote in a note to clients on Tuesday. "This highlights the broad risks around reopening."

And those risks will cause businesses and consumers to remain cautious for the foreseeable future. People will be reluctant to travel, go to business conferences, sit cheek-by-jowl in ballparks, visit amusement parks or even eat at restaurants.

"Life is not going back to the way it was until we get a vaccine," Boockvar said.