The Trump administration’s plan to provide every nursing home with a fast COVID-19 testing machine comes with an asterisk: The government won’t supply enough test kits to check staff and residents beyond an initial couple of rounds. A program that sounded like a game changer when it was announced last month at the White House is now prompting concerns that it could turn into another unfulfilled promise for nursing homes, whose residents and staff represent a tiny share of the U.S. population but account for as many as 4 in 10 coronavirus deaths, according to some estimates.