Washington (CNN) While President Donald Trump and some major companies are looking ahead to reopen businesses, the groups that are giving the country medical care and keeping Americans fed say they're not ready.

Shortages of essential coronavirus supplies exist at every layer of the American economy, from hospitals on down. And the most critical items needed for states to lift their shutdown orders -- including testing and tracing of coronavirus cases, thermometers for screening customers and workers, even cloth masks for people to wear at work or outside -- are not widely available, even to essential businesses, according to industry groups that represent manufacturers, food production companies, labs and hospital groups.

Over the past month, state shutdowns have allowed some essential businesses to gradually get what supplies they need to operate and formulate plans. The country's top infectious disease doctor, Anthony Fauci, warned during an interview on "Good Morning America" Monday that reopening businesses too soon could "backfire." Some manufacturers whose production lines are maxed out already fear even a gradual return to normal commerce could be catastrophic.

"I get very concerned in the absence of clear messages from the federal government that we're going to create a situation that looks a little more like the Wild West," Geoff Freeman, who leads the Consumer Brands Association, told CNN on Friday.

"Reopening isn't the problem. Reopening without a plan is the problem," Freeman said. His industry group represents major grocery goods companies like Clorox, General Mills, Kellogg and Target, that, as he says, supply the products in aisles 1 through 12 of every grocery store and also manufacture food and cleaning products for other companies, like restaurant chains.

If states were to lift their lockdowns, "you're putting the strains on this situation at a time we can't afford," he said.

The White House last week gave governors advice on how they could begin reopening businesses and lifting stay at home orders, and some large companies like Starbucks and Boeing announced to their employees they were looking ahead to a gradual return to normal. Small groups protesting state stay-at-home orders have erupted across the country as well, but local authorities have criticized those protests as potentially encouraging the spread of the virus before it can be controlled

As soon as offices, restaurants and other spaces start reopening, the shortages for protective equipment will spike even more than they are now, especially if coronavirus cases begin increasing again.

In recent days, a Smithfield pork processing plant closed after employees fell ill with coronavirus, raising concern about the meat supply across the country.

"We can't figure out how to get cloth masks," Freeman said. "If we think we have problems now, imagine a situation where people didn't have confidence in access to essential products."

Contactless thermometers, another key item for reopening more of the American industry, are already in short supply. Food manufacturers don't yet have as many as they've ordered. If workplaces and restaurants reopen, they'll be ordering thermometers as well.

ThermoWorks, which makes no-touch thermometers, has already noticed companies anxious to reopen and want to put temperature screening in place for employees.

"The hardest thing is they're in a hurry," ThermoWorks CEO Randy Owen said of companies placing orders. "Some of them are hopeful that that on May 1 they'll be able to open some units. And so they're trying to get stock in hand by May 1, and that's exceptionally difficult right now because nobody has any -- and what they do have is sold out."

Owen said part of the shortage stems from infrared instrument factories in China, which were prohibited to export what they made until only recently.

Even masks -- a cornerstone item to prevent the spread of the virus -- aren't available yet widely.

Jay Timmons, head of the National Association of Manufacturers, noted that several categories of essentials, from medical supplies, to personal protective equipment, to cleaners and wipes, are still in high demand. Manufacturers are working on making more, he said, and industries outside of health care and manufacturing, which are already relying heavily on the supply to stay operational, will have their own "massive need," he said.

According to one large food company, FEMA was sweeping up cloth masks from plants where they were being made as recently as 10 days ago, causing delays for some essential employers to get as many as they sought.

"It turned out we were all fighting for the same personal protective equipment," said one supply chain head at a major food manufacturer, who asked to be named as not to face consequences from government agencies.

That company now has orders placed for protective items and for thermometers to use in employee screenings at plants. The thermometers haven't been delivered yet. "You just never know if it's actually going to come true or not," the executive said.

Even testing, the number one requirement for controlling the epidemic, according to health officials, is not readily available, even to hospitals. Labs themselves are struggling to get supplies to run more tests.

Trump bragged on Sunday during his daily coronavirus briefing that lab supplies were easy to get, then almost immediately appeared to respond to the shortages by ordering a Maine company to increase its production of swabs used by labs

But governors of both parties have been explaining how their states are facing extreme shortages in supplies, especially for testing. Several governors, from Virginia, California, New York and Ohio, pleaded for more swabs and other supplies in media appearances over the weekend.

"We have a shortage, worldwide shortage, of some of the materials that go into this," Ohio Republican Gov. Mike DeWine said on NBC's "Meet the Press." "So, we really need help -- if anybody in the FDA is watching, this would really take our, take our capacity up, literally Chuck, overnight."

Demand for swabs, in fact, has far exceeded the supply.

Last week, labs had placed orders for 2.5 million swabs through its main supplies artery. Yet only 200,000 swabs were in stock, according to the Association of Public Health Laboratories this week. The American Hospital Association also noted that testing is still facing critical supplies shortages, with not enough swabs, transport media or reagents available to health care systems.

"We are doing everything we can to ramp up production to help meet the demand," Dr. Thomas Theuringer, a spokesman for Qiagen, a Covid-19 test kit manufacturer, said in an email to CNN. But the demand is still challenging the industry.

The company is sending out partial shipments or delaying orders. They're ramping up production -- from test kits that could cover 1 million patient samples in February, to more than 3 million in March, to 7 million this month.

But the demand is so large. By October, the company hopes to be handling 20 million patient samples a month.