'I've felt no vulnerability whatsoever,' Trump said of White House staffer infection and mask decree

President Trump pushed back Monday on the idea that White House procedures to keep out the coronavirus have failed – after two internal staffers in recent days tested positive for the virus.

"I've felt no vulnerability whatsoever," Trump said at a Rose Garden press conference. "I don't think the system broke down at all. One person tested positive, surprisingly, because the previous day tested negative. And three people that were in contact, relative contact, who I believe they've all tested totally negative. But they are going to, for a period of time, self-isolate. So that's not breaking down. It could happen, it's the hidden enemy. Remember that, it's the hidden enemy."

Trump spoke just hours after the White House required all staffers to begin wearing face masks when walking on the grounds and between offices.

Last week, a White House military valet and Kate Miller, a spokesperson for Vice President Pence, tested positive for the virus.

"You know, we have a lot of people at the White House, and we had one, basically, we had one person," Trump continued Monday. "We have a lot of people that work there. This building is shocking, if you looked at the numbers."

"America Leads The World In Testing," a banner sign read behind Trump during the press conference, where he was flanked by coronavirus testing machines set up on tables on either side of his speaker rostrum. Journalists and White House press staffers were wearing masks during the press conference.

America has now conducted nearly 9 million tests, and Trump said the country will pass the 10 million mark this week. Trump said testing is now up to four times more per capita than in other major countries per capita UK, Japan, Sweden, South Korea, and Finland.

"In the span of just a few short months, we've developed a testing capacity unmatched and unrivaled anywhere in the world," he said. "And it's not even close. This is a core element of our plan to safely and gradually re-open America. And we're opening, and we're starting, and there's enthusiasm like I haven't seen in a long time."

Adm. Brett Giroir, sssistant secretary for Health, Department of Health and Human Services, said the federal government would be sending $11 billion to U.S. states, territories and tribes for testing. 

"Most states are doing a great job," Trump said.

Giroir said there will be enough tests to "allow us to take this country safely through phase one” of the White House's reopening guidelines.

Trump said testing goals and projections for each state totaled 12.9 million tests during the month of May. Trump said FEMA would ship 12.9 million swabs to states nationwide. 

"Germany and the United States are leading the world in lives saved per 100,000," he also said. 

Mortality data from the Johns Hopkins University Coronavirus Resource Center show that the U.S. has fewer deaths per capita than than Belgium, France, Italy, Netherlands, Spain, Sweden and the United Kingdom, with far lower coronavirus-deaths-per-100,000 population. 

The U.S. death rate  for coronavirus is lower than many European countries, yet 38% of American voters think the United States is doing a "worse job" in handling COVID-19  according to a new Just the News Daily Poll with Scott Rasmussen. 

Trump said his administration had partnered with the private sector for the distribution of 90 million N-95 masks, 126 million surgical masks, 9 million face shields and 21 million surgical gowns.