WASHINGTON—President Joe Biden on Tuesday moved up the COVID-19 vaccine eligibility target for all American adults to April 19, but warned that with new virus variants spreading “we’re still in a life-and-death race” with the coronavirus. Biden directed states to widen the vaccine eligibility to people 18 or older by April 19, two weeks earlier than the May 1 deadline he announced previously. No COVID-19 vaccine is authorized yet for children under 16, although testing is underway. Most states had already said they would open vaccines to all adults by that new target date. “What we do now is going to determine how many people we’ll save or lose in the month of April and May, and June, before we get to July Fourth,” Biden said at a White House event. More than 80 percent of teachers and school staff had received at least one vaccination shot, Biden said, but …