Trump touted reopening. Privately, his team sounded alarms.

President Donald Trump boasted on May 1 that his success in responding to the coronavirus pandemic has made ventilator, test kit and mask shortages a thing of the past, and that much of the country is ready to quickly send people back to work.

“We’ve ensured a ventilator for every patient who needs one,” he said. “The testing and the masks and all of the things, we’ve solved every problem. We solved it quickly.”

But that same day, his own health and emergency management officials were privately warning that states...