Employers grapple with tough new question: Can they demand workers get a COVID-19 vaccine? • 8 min read Why are people hesitant to trust a COVID-19 vaccine? Vaccines are proven to reduce deaths and help end pandemics, but the historic speed that the coronavirus vaccines have been developed has made some people hesitant to take them.Mario Tama/Getty Images. FILE As the rollout of the COVID-19 vaccine expands across the country, experts tell ABC News that employers in high-risk industries have begun to wrestle with a new and vexing question: Can a company require its employees to be vaccinated? Some employees have already begun to push back on the idea. First responders in New Mexico have sued after a county official ordered firefighters, corrections officers and other first responders to receive injections. And at the 120-bed Rock Haven Nursing Home in Wisconsin, 21 employees quit after nursing home administrators and county officials issued a vaccine mandate for the staff.