If President Trump announces that North Korea launched a missile that landed within 100 miles of Hawaii, would most Americans believe him? Would the rest of the world? We’re not sure, which speaks to the damage that Mr. Trump is doing to his Presidency with his seemingly endless stream of exaggerations, evidence-free accusations, implausible denials and other falsehoods.

The latest example is Mr. Trump’s refusal to back off his Saturday morning tweet of three weeks ago that he had “found out that [Barack] Obama had my ‘wires...