Inside Northwell Health's year-old, $60-million US lab, located in an old military complex outside New York City, Dr. Dwayne Breining and his team are eager to start testing for COVID-19. But because of government missteps, they're still in a holding pattern.

Until this past week, local labs like this were essentially shut out of the testing process, which was initially centralized at the Centers for Disease Control and Prevention in Atlanta.

Breining says with his state-of-the-art equipment they could process hundreds, or possibly thousands, of potential COVID-19 samples a day once an automated test is developed.

"In retrospect, you always think you could have done things better than they'd been done, and I think everybody would say that right now," said Dr. Dwayne Breining, executive director of Northwell Health.

Breining says testing should ramp up soon, because last weekend, the Food and Drug Administration relaxed regulations to allow private companies and labs to begin developing faster testing for COVID-19.

WATCH: Dr. Dwayne Breining explains his lab's capacity for coronavirus testing:

Critics say the U.S. government’s response to the coronavirus outbreak was slow, downplayed the threat and could have worsened the spread. 1:56

But even then, rapid testing is still potentially weeks away.

"I think it's safe to say we wish we could have rolled out the testing a lot faster," Breining said.

This week, administration officials have scrambled to reassure Americans that tests would be more readily available. On Thursday Vice-President Mike Pence admitted: "We don't have enough tests today to meet what we anticipate will be the demand going forward."

After Pence promised that 1.5 million tests would go out this week, Secretary of Health Alex Azar said Friday that the CDC and its private contractor have shipped close to 800,000 tests. More are scheduled to arrive next week.

'What a ridiculous and uneducated response'

Critics say testing issues began in January when the CDC chose not to use the German-engineered test being distributed by the World Health Organization and instead worked on developing its own.

In February, the CDC sent out test kits to state and local labs, but those turned out to be faulty. A replacement took weeks.

There's also criticism over the narrow criteria for who got tested. The CDC limited to only those who had travelled to a hotspot, potentially missing a large number of cases and allowing the virus to circulate undetected along a larger population for weeks, critics say.

The rules were only relaxed this week. A congressional committee has said it will investigate.

On Thursday, a nurse in Northern California said she was refused testing by the CDC even though she developed symptoms after caring for a patient that later tested positive for COVID-19.

U.S. Vice-President Mike Pence, who heads the federal government's coronavirus task force, shown here greeting a woman at the Washington State Emergency Operations Center Tacoma, Wash., on Thursday, promised 1.5 million coronavirus test kits would be sent out this week. But only 800,000 went out. (David Ryder/Reuters)

"They said they would not test me because if I were wearing the recommended protective equipment, then I wouldn't have the coronavirus. What kind of science-based answer is that?" the nurse said in a statement released by her union, National Nurses United.

"What a ridiculous and uneducated response from the department that is in charge of our health in this country."

Critics say cutbacks, Trump to blame

The Trump administration's "chaotic'' response to COVID-19 is the result of an inability to marshal government resources effectively, and the responsibility lies with the president himself, according to health policy analyst and journalist Laurie Garrett.

"We're in such a crude state of affairs with developing our ability to do surveillance and diagnosis, it's pathetic," said Garrett, a Pulitzer prize-winning author of books such as The Coming Plague.

WATCH: Laurie Garrett criticizes the U.S. response to coronavirus:

The U.S. has not been investing in public health system, leaving it poorly equipped to handle an outbreak, says Laurie Garrett of the Council on Foreign Relations 0:55

She points to accelerated and efficient testing in China and South Korea as examples of how the U.S. has lagged behind the rest of the world.

One estimate suggests the U.S. has tested fewer than 2,000 people, compared to tens of thousands in other countries.

"We're the scientific leader of the planet. The National Institutes of Health budget dwarfs every other in the world. We're the one that's always going out, telling other countries what to do and how to do it in an epidemic. And we're just lost."

Garrett said cutbacks to public health budgets are partly to blame, but also a president whose first instinct was to politicize the criticism over his administration's handling of the outbreak, and constantly undermine his experts.

'We have no clue how widespread this virus is in America'

During a visit to CDC headquarters in Atlanta on Friday, Trump called Washington Gov. Jay Inslee, who is handling the largest outbreak in the country, a "snake." He also dismissed criticism that tests aren't available.

"Anybody that wants a test can get a test," Trump said. He compared the quality of the testing to the phone call with Ukraine's president that led to his impeachment.

"The tests are all perfect, like the letter was perfect, the transcription was perfect. This was not as perfect as that, but pretty good."

And while Trump said no one could have seen this outbreak coming, Garrett said the administration had weeks to plan as China dealt with the initial stages of the virus.

"We had a good seven weeks warning, a window in which to prepare and get the government organized and they did nothing. Where does the fault lie? Well, there's no answer except it goes to the top. It's the Oval Office."

Trump also touted the low number of overall cases as a sign of the government's success. The president even said he'd prefer passengers stuck aboard a cruise ship off the coast of California with a number of COVID-19 cases remain onboard so as not to raise the overall American case count.

"I like the numbers being where they are. I don't need to have the numbers double because of one ship that wasn't our fault," he said.

Garrett said it's impossible to know the virus's true footprint in the U.S. without widespread testing.

In a perfect world, she said, the government would go into hospitals and nursing homes and test anyone with suspicious symptoms to gain an understanding of what cases may be hidden.

"Until we do such things … we have no clue how widespread this virus is in America. We have absolutely no idea," Garrett said.

Testing capacity is still limited. The Association of Public Health Laboratories said there are currently 69 local and state public health labs verified to do testing across 46 states. Each lab can currently process about 100 tests per day.

Staff members at Northwell Health Labs in Lake Success, New York, demonstrates how a patient is tested for COVID-19. Some health critics say the United States made it too difficult for people to be tested. (Steven D'Souza/CBC News)

Further hindering public health officials' ability to get a grasp on the true number of cases in the U.S. is the close to 30 million Americans who lack health insurance and may balk at getting tested. One report suggests tests could cost upwards of $3,000 US.

The president signed an $8.3-billion US spending package Friday. But it's not clear how much will go to subsidizing the costs of tests. Some money will be allocated for testing and vaccine creation.

Breining at Northwell Health hopes some money will trickle down to them. He said they've spent $5 million US so far upgrading equipment to tackle COVID-19.

"We've got everybody here working overtime. We're getting new equipment in here. It all needs to happen pretty quickly; it all costs money. So the more resources we have, the better we'll be able to do that."