WASHINGTON — The Covid-19 vaccine had finally come to Forest Hills of D.C., a nursing home in a prosperous neighborhood of the nation’s capital, but there was a problem. Though nearly all of the home’s residents agreed to get the shots, nearly half its 200 staff members declined.

Tina Sandri, the chief executive, vowed not to let those numbers stand.

Over the next two months, rounding out the most bruising year of her long career in elder care, Ms. Sandri tried everything. She bombarded employees with text messages containing facts about the science behind the vaccines. She assigned a popular young worker to try to sway reluctant colleagues as an “influencer.” She set up a giant screen to show a television special that the Black actor and director Tyler Perry made to fight vaccine hesitancy — on a continuous loop, no less. Most of all, she worked to understand their concerns.

“You really have to listen to each person’s story and address it from that standpoint, so they feel, ‘This is a workplace that cares about me,’” she said.

Scientists view Florida — the state furthest along in lifting restrictions, reopening society and welcoming tourists — as a bellwether for the nation.

If recent trends there are any indication, the rest of the country may be in trouble.

The number of confirmed coronavirus cases in Florida has been steadily rising, though hospitalizations and deaths are still down. Over the past week, the state has averaged nearly 5,000 cases per day, an increase of 8 percent from its average two weeks earlier.