Just over 4 million tests have been completed so far, for a population of roughly 330 million Americans, amid widespread reports of sick Americans being unable to get tested quickly — increasing the odds of spreading the virus. Estimates vary widely even among reputable public health experts about how many tests need to be done to keep the virus at bay. The White House‘s numbers are on the low end of that spectrum.

But administration officials are expressing confidence in public and private that the U.S. has enough tests for the short term and will have enough for the summer, since not every American needs to be tested.

The challenge could come in the fall, said a senior administration official and a third Republican close to the White House, when flu season returns and patients flood doctors’ offices with symptoms that could be Covid-19 or the flu. Doctors and labs will need tests then to make a distinction.

But many administration officials now privately acknowledge that pledges from Trump and his team since early March have not panned out, even as Trump continues to hype the administration’s early work.

During a visit to the Centers for Disease Control and Prevention in Atlanta on March 6, the president told reporters “anybody that wants a test can get a test. That’s what the bottom line is.” His comment was contradicted for the past six weeks by state officials, health care workers and countless individual stories of Americans unable to get tested.

By March 12, senior adviser Jared Kushner had started to get involved in the coronavirus efforts — at the urging of the vice president’s chief of staff, Marc Short — because internally the development of tests was viewed as a mess. Kushner stood up a separate operation at the Federal Emergency Management Agency apart from the coronavirus task force, sending White House and health aides to work out of the FEMA headquarters.

Trump has made other announcements — such as widespread testing by companies in parking lots — that he then mocked as outside the federal government’s responsibility.

The White House’s coronavirus response coordinator, Dr. Deborah Birx, said Friday the administration’s job was to support states and lab directors to help them ramp up testing and take full advantage of the nation’s existing capacity. One White House official said Friday’s briefing laid out the White House’s testing strategy and showcased the role the administration intends to play: as air traffic controllers to help states land supplies.

Trump and other top aides have said the testing and resources for them are up to the governors.

Even the question of who within the White House is the point person on testing remains unclear internally to staffers. A top Health and Human Services official, Adm. Brett Giroir, is officially the testing czar. Kushner has been involved since mid-March to add urgency to the effort. Birx is also working on ramping up testing capacity out of Walter Reed National Military Center.

Coronavirus task force officials acknowledge early missteps on testing, even as Trump’s closest aides try to portray it as a problem they’ve solved.

“No doubt that, early on, we had a problem. I had publicly said that we had a problem early on. There was a problem that had to be corrected, and it was corrected. It was a problem that was a technical problem from within that was corrected,” Dr. Anthony Fauci said at Friday’s White House briefing.

“And it was an issue of embracing — the way we have now, and should have — the private sector, who clearly has the capability of making and providing tests at the level that we will need them for,” Fauci added.

The lag in testing comes in part from the president and the administration’s early efforts to downplay the threat of the virus, along with changes in leadership on the coronavirus task force and early missteps by the CDC to develop a test.

Roughly 15 weeks after the coronavirus appeared in China and on the radar of White House staff, states say they still lack the capacity to test every resident with symptoms — let alone the people potentially harboring the virus without exhibiting signs of illness.