New York's scramble to find enough breathing machines to treat its rapidly expanding legion of coronavirus patients illustrates a problem vexing hospitals and governments worldwide.

In his nationally televised briefings this week, New York Gov. Andrew Cuomo has made desperate pleas to other states and the federal government to send breathing machines that the state will return when demand slows down.

Cuomo's plea has proven to be a tough sell. For one, the devices are already in short supply nationally. And medical professionals and officials in other states are expecting to be inundated with coronavirus cases themselves relatively soon. They aren't easy to quickly manufacture either, despite efforts underway by several major companies.

The machines also known as ventilators are necessary for severely ill patients, and there aren't enough to meet the projected needs as the virus spreads.

Compounding the problem is the fact that doctors say coronavirus patients often need ventilators for weeks, if not longer — slowing the hand-off from one patient to the next. It's the same problem that China and Italy have also faced with no easy solution.

Cuomo said this week his state has 4,000 ventilators and has purchased another 7,000. The U.S. government has pledged to send New York another 4,400 ventilators. That's still far short of the 30,000 ventilators that Cuomo said the state will need if the crisis reaches its expected breaking point in New York, which has emerged as a virus hotspot.

In an interview Thursday night with Fox News Channel's Sean Hannity, President Donald Trump dismissed Cuomo's estimates.

“I don't believe you need 40,000 or 30,000 ventilators,” Trump said.

In the meantime, New York is converting a couple thousand anesthesia machines they have into makeshift ventilators and adding a second set of tubes to some ventilators so each one can be used for a two patients.

“It's not ideal, but we believe it's workable,” Cuomo said.

The American Society of Anesthesiologists disagreed, saying in a statement that sharing a breathing machine for two people is dangerous and could prevent both patients from benefiting because “ventilation needs to be individually tailored and monitored continuously.” The group did back New York's use of anesthesia machines.

At present, U.S. hospitals have roughly 65,000 ventilators that are fully capable of treating severe coronavirus patients. But they could cobble together about 170,000, including some simpler versions that won't work in all cases, said Dr. Lewis Rubinson, chief medical officer at Morristown Medical Center in New Jersey and lead author of a 2010 medical journal article on the matter.

In a February presentation for other medical professionals, Dr. James Lawler, an associate professor and infectious disease specialist at the University of Nebraska Medical Center, estimated that 960,000 people in the U.S. will need to be on ventilators.

Rubinson said it’s unlikely the U.S. would need that many ventilators at the same time, estimating it will need more like 300,000 fairly quickly. If social distancing works, people will catch the virus at different times, allowing hospitals to use ventilators multiple times.

“This is the whole reason why everyone talks about flattening the curve,” he said.

He estimates there are seven or eight ventilator makers in the world, and together they can crank out several thousand per month, far short of global demand.

In the most severe cases, the coronavirus damages healthy tissue in the lungs, making it hard for them to deliver oxygen to the blood. Pneumonia can develop, along with a more severe and potentially deadly condition called acute respiratory distress syndrome, which can damage other organs.

Ventilators feed oxygen into the lungs of patients with severe respiratory problems through a tube inserted down the throat. The machines are also used routinely to help other hospital patients breathe, namely those undergoing surgery while under general anesthesia.

In China, where the virus first emerged, factories worked nonstop for about a month to try and produce ventilators but were initially held back by shortages of raw materials, according to Chinese media reports. They received the needed materials through donations, fundraising drives and charities. Some ventilators were purchased overseas. Finally on March 4, after at least 15,000 had been delivered to the province of Hubei, where the outbreak was concentrated, government officials declared there were enough to meet the province’s basic needs.

Several companies around the world are trying to make the breathing machines, but it takes time.

At Dyson, the British company best known for making vacuums, a team of engineers has been working on a design for the last 10 days since receiving a request for help from Britain Prime Minister Boris Johnson. Billionaire inventor James Dyson told his staff the device would draw on technology used in the company's air purifier ranges and is powered by a digital motor. Britain wants to increase the availability of ventilators from 8,000 to 30,000.

U.S. automakers General Motors and Ford, teaming with ventilator makers, have hundreds of people working almost around the clock trying to make more of the life-saving devices. GM plans to start building test versions in early April, eventually making 20,000 per month.

Ford CEO Jim Hackett said this week that by mid-May, Ford should be manufacturing a ventilator with GE Health Care. He said all companies that make ventilators in the U.S. and Europe could be producing at a rate of 900,000 per year by June.

Experts say no matter how many they make, the number probably won’t be enough to cover the entire need, and it may not come in time to help New York or other areas now being hit hard with critical virus cases.

General Motors is gearing up to make ventilators at an electronics plant in Kokomo, Indiana, but it hasn’t given definitive numbers or a date to start production.

Tesla and SpaceX CEO Elon Musk has said on Twitter he’s talking with ventilator maker Medtronic about manufacturing the devices, but company spokesmen didn’t return messages seeking details.

Even if automakers and others start producing in May or June, any ventilators they make still will save multiple lives because they can be used to help two or more people, said Dr. Jack Iwashyna, a professor of internal medicine at the University of Michigan.

“The fact that you can't save everybody doesn't mean you shouldn't save some,” he said.

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AP researcher Yu Bing in Beijing, and Marina Villeneuve in Albany, New York, contributed to this report. McCombs reported from Salt Lake City and Krisher from Detroit.