Later on in the briefing, Alexander asked the exact same question of Vice President Mike Pence.
"What do you say to Americans right now who are watching right now and scared?"
"I would not say, do not be afraid, be vigilant," the Vice President said, handling the question without taking any jabs at reporters in the Briefing Room.
In real time before reporters, and a national viewing audience, the President talked up the use of the malaria drug chloroquine as a possible way to address to the Coronavirus - only to then hear Dr. Anthony Fauci say the evidence that it could be of help was only anecdotal.
Fauci said there was no scientific evidence that chloroquine could fight a virus like SARS; the President then said it could be a 'game changer.'
Pressed by reporters about a lack of Coronavirus tests - which several Governors complained about during a conference call with the President on Thursday - President Trump repeatedly talked instead about not testing all Americans, before finally rejecting the premise of the question.
"There are Americans who say they have symptoms and they can't get a test," one reporter said, the questions coming two weeks after the President said at the CDC that anyone who wants a test, can get a test.
"I'm not hearing it," Mr. Trump responded, blaming testing troubles on the Obama Administration, and jabbing at the reporter for asking the question.
Once again, Fauci had a different take.
"That is a reality that is happening now," Fauci said of the inability of some with symptoms to get tests. "Is it the same as a few weeks ago? Absolutely not."
The President also went round and round with reporters on his move to invoke the Defense Production Act, in order to get major American industries to help produce needed medical items like ventilators.
Mr. Trump invoked the law earlier this week, but seemed to indicate he was waiting to use it, and then tussled with reporters about whether he had, and what it would produce.
The President also announced the U.S. was shutting down the southern border with Mexico, prohibiting most travel except for trade between the two nations.