President Donald Trump declared Tuesday that the U.S. will be able to carry out five million coronavirus tests per day, but the top official overseeing testing strategy told TIME earlier in the day that goal wasn’t feasible given current technology.

Admiral Brett Giroir, the assistant secretary of health who is in charge of the government’s testing response, said during an interview on Tuesday morning that “there is absolutely no way on Earth, on this planet or any other planet, that we can do 20 million tests a day, or even five million tests a day.”

Since the beginning of the year, the Administration has conducted 5.7 million tests in total, he said. And while the government has made strides in increasing the number of tests being performed in recent months, the White House’s new “blueprint” for testing, rolled out on Monday, currently plans to double current COVID-19 testing. Giroir plans to hit 8 million per month by next month.

The tally would still fall short of what a Harvard University study said is necessary to safely restart public life. The 56-page “roadmap” published last week by a group of experts said the U.S. needed to be capable of carrying out at least 5 million tests a day by early June, and 20 million per day by late July, in order to reopen the economy. Giroir called the assessment “an Ivory Tower, unreasonable benchmark,” that wasn’t needed, based upon current modeling projections, and that couldn’t be supported by current technology.

Five hours later, when a reporter asked Trump at the White House if the country would reach five million daily tests, as the Harvard study recommended, Trump responded: “We’ll increase it, and it’ll increase it by much more than that in the very near future.” Asked to clarify if he meant the U.S. would “surpass 5 million tests per day,” Trump said, “We’re going to be there very soon.”

The largest number of tests conducted by the U.S. in a single day was 314,182, according to Covid Tracking Project data. Trump didn’t offer how his Administration was going to account for the 1,500% increase, but assured those at the briefing: “If you look at the numbers, it could be that we’re getting very close.”

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Trump’s assertion was the latest in a series of inaccurate and misleading statements made by the president about the COVID-19 crisis that have often placed him at odds with the experts advising him. On Feb. 28, speaking about the new coronavirus, he declared “like a miracle, it will disappear.” On March 6, he said that “anybody that wants a test can get a test”. Last week, bizarrely, he speculated that “ultraviolet” light or the injecting of disinfectants might serve as treatments.

In the absence of a vaccine or effective treatment of the new coronavirus, testing is a crucial element in any plan to allow Americans to return to their normal lives, experts say. Trump’s apparent lack of familiarity with his own Administration’s testing plans is the latest of a series of costly missteps on that front. In January, the Centers for Disease Control and Prevention distributed hundreds of faulty diagnostic test kits. Then in February, the Federal Food and Drug Administration was too sluggish in approving tests developed by hospital, university and private laboratories, creating a bottleneck.

The Administration has been able to streamline those processes over the last two months and build up capacity, but as labs and states now compete for the same equipment, a new problem has emerged: a scarcity of supplies.

The White House has repeatedly celebrated advances in boosting U.S. testing capacity and expressed confidence about states’ ability to do more in hopes of getting closer to Trump’s foremost goal: a phased reopening of the economy. As state and local governments consider re-opening, public health experts agree it will take meticulous and widespread testing to identify people who might be infected, trace their contacts, test those individuals who came in contact with an infected person and isolate them from the public to reduce the chances they will spread the virus.

The 5.7 million tests conducted in the U.S. so far are much more than any other country, but represent less than 2% percent of the total U.S. population. The Administration’s testing blueprint, announced Monday by the President in the White House Rose Garden, outlines how the federal government aims to help all 50 states.

Giroir, a pediatric critical care specialist who previously served in roles at the Defense Department, said all states require a tailored strategy and that their individual testing plans will be dependent on a range of factors, including the “virus circulating within their states as well as the particular demographics.” The goal is for each state to be able to screen at least 2% of their residents, he said.

The Administration works with states on a weekly basis to discuss their specific needs, review the testing strategies, and follow-up on any additional requests they may need. “If we do testing in a smart way, like all those who were symptomatic and contact-traced and you targeted asymptomatic screening, that’s really the way to go,” Giroir said.

Experts say the U.S. has not done enough testing to yield an accurate and actionable picture of the epidemic for states to come up with effective plans. “If a state misjudges its true underlying infection trajectory, it may suffer large flare-ups of the disease, necessitating a long and painful lockdown again,” wrote Dr. Ashish Jha, director of the Harvard Global Health Institute. “Yet most states are long way from adequate testing—and the tracing of contacts that must follow.”

The U.S. has increased the number of tests as commercial testing companies increase production and the Food and Drug Administration continues to approve tests using different types of samples, including ones from the nose and saliva, as well as blood. States are responsible for developing their own plans to secure those tests from companies, Giroir said, while the federal government should be the “supplier of last resort.”

“It’s horribly inefficient to say that the government is going to buy all the supplies, recreate a distribution center, do 5,000 hospitals, maybe 10,000 laboratories in academic centers,” Giroir said. “What we really want to do is use the commercial supply chain.”

Senator Patty Murray of Washington, the top Democrat on the Health Committee, took issue with this aspect of the Administration’s testing blueprint because individual states are already fighting with one another to obtain much needed medical supplies. The Trump approach doesn’t “identify ways to fix our broken supply chain, or offer any details whatsoever on expanding lab capacity or activating needed manufacturing capacity,” she said in a statement on Monday. “Perhaps most pathetically, it attempts to shirk obvious federal responsibilities by assigning them solely to states instead,” she said.

Governors from the hardest-hit states say they’re locked into counter-productive bidding wars with one another to acquire certain supplies, including tests. Maryland Governor Larry Hogan was so desperate for diagnostic testing kits, he bought half a million kits from a South Korean company. Politicians, medical professionals and hospital officials have criticized Trump’s reticence to ease the supply shortage by using presidential authorities under the Defense Production Act (DPA) to compel U.S. private production capacity to manufacture the supplies.

Giroir said that kind of criticism is “based on very little knowledge of how this works.” For instance, testing swabs have been in short supply since March. The swabs—which resemble oversized Q-tips and are inserted into the nose to sample mucus at the top of the throat—are manufactured in northern Italy and China, where production was decimated due to coronavirus outbreaks. “Like if you were relying on one swab type that’s only made in Italy, because that’s what the FDA does, it doesn’t matter what I do [in the U.S.] until you open the market and have different swab types,” Giroir said.

Due to the scarcity of key testing components like swabs, chemical reagents and tubes, Giroir acknowledges that the federal government needs to help steer some critical parts of the supply chain to increase the number of tests being done. In May and June, the federal government plans to purchase the components necessary to meet all the states’ plans and distribute them to central locations in each state.

“For swabs and tubes, it’s really the heaviest hand of the federal government,” he said. “We buy it, we procure it, we know it’s there, we ship it. But over the course of the summer, by July, we think we’re going to move even the swabs and the tubes into a more directed traffic-controlled free market system, where we don’t buy it, but we assure the states can purchase what they need for every single line.”

Come this summer, he said, “We’ll be swimming in swabs.”

When reached after the President’s comments, Giroir’s staff said the Administration is always looking for ways to ramp up testing but maintained that—barring technological breakthrough—5 million tests could not be supported.

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Write to W.J. Hennigan at william.hennigan@time.com.