Anthony Fauci Anthony FauciOvernight Health Care: US coronavirus deaths hit 200,000 | Ginsburg's death puts future of ObamaCare at risk | Federal panel delays vote on initial COVID-19 vaccine distribution White House seeks to change subject from 200K COVID-19 deaths Putin calls on UN to strengthen World Health Organization MORE on Tuesday said he hoped anyone who needed a coronavirus test should be able to get one by the end of May or early June.

“Hopefully we should see that as we get toward the end of May, the beginning of June,” Fauci said when asked by CNN’s Jake Tapper Jacob (Jake) Paul TapperJulia Louis-Dreyfus: 'We can't spend much time grieving' Ginsburg Pence aide dismisses concerns rushed vote on Trump nominee will hurt vulnerable senators Klobuchar: GOP can't use 'raw political power right in middle of an election' MORE, “When will everybody who needs to get a test be able to get one?”

“That's what I'm being told by the people who are responsible for the testing,” said Fauci, the government’s top infectious disease expert, referring to his colleagues on the White House task force dealing with the pandemic.

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"I take them for their word. If that doesn't happen, I'm gonna go to them and say, 'What happened here? Why didn't it happen, and how can we fix it?'"

Fauci said the assurances are coming largely from Adm. Brett Giroir, the assistant secretary of Health and Human Services, who has been helping lead testing efforts.

“As we get into May and June, from what we're hearing, and I'm telling you, Jake, what we're hearing from the people in the task force who deal directly with the companies, namely the major firms that make the tests, this is predominantly Adm. Brett Giroir, is telling us that we will have a very, very increased production so that by the time we get to those months, we should have what we need,” Fauci said.

“But I'm always the skeptic in the group,” he added. “And I always say, ‘OK, I hear you, I believe you, but let's see what happens.’”

Giroir said at a White House news conference on Monday that the U.S. would “easily” conduct 8 million tests in May.

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That level would still fall short of what many experts say is needed. Fauci has previously said the U.S. needs about 3 million tests per week, or 12 million per month. Harvard researchers say 500,000 tests per day, or about 15 million tests per month, are needed.

The White House pointed to announcements from companies such as CVS and Walgreens on Monday that they will be significantly expanding testing availability at their stores across the country.

President Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE has made bolder claims on testing. In March, he said that “anybody that wants a test can get a test,” though testing problems have continued since that statement.

On Tuesday, he said in response to a question that the U.S. would “very soon” have the capacity to test 5 million people each day, though the country is currently testing about 200,000 per day.