With just days or even hours to spare, thousands of health care workers got inoculated, according to health officials across the state. And while thousands more workers remained unvaccinated, and thus in danger of being suspended or fired, the rush of last-minute vaccinations appeared to blunt the worst-case scenarios for staffing shortages that some institutions had feared.

In the New York City public hospital system, more than 8,000 workers were unvaccinated a week ago. But by Monday morning, that number had dropped to 5,000 — or just over 10 percent of the work force. Although those unvaccinated employees were not permitted to work, city officials said they felt they could manage the gaps.

In Rochester, officials at Strong Memorial Hospital placed a two-week pause on scheduling elective procedures and warned patients to expect longer wait times for routine appointments as the deadline loomed last week. But on Monday, they announced that they were able to bring up their staff vaccination rate to 95.5 percent from 92 percent last week, meaning that fewer than 300 employees out of 16,000 will be fired if they don’t relent.