Thousands of unvaccinated hospital employees in New York are likely to lose their jobs with a statewide vaccine mandate kicking in Monday night at midnight, the first major test of such rules for health-care workers nationwide.

Several hospitals have warned that the requirement, announced in August, is already causing staff shortages that will force them to curtail patient care. Gov. Kathy Hochul (D) has called such issues “completely avoidable” and said she is prepared to activate the National Guard or recruit health-care workers from elsewhere to fill the gaps.

On Monday, Hochul delivered a final plea to unvaccinated health workers ahead of the deadline. “Please do the right thing,” she said at an event in New York City.

New York’s experience will be watched closely throughout the country. It is one of six states — with Colorado, Maine, Oregon, Rhode Island and Washington — to announce that health-care workers must be vaccinated against the coronavirus or face termination. It also instituted the earliest deadline nationwide.

Several other states, such as California, Pennsylvania and Massachusetts, have announced that health-care workers must either get vaccinated or submit to regular coronavirus testing.

About 84 percent of New York’s 450,000 hospital workers were fully vaccinated as of Sept. 22, according to the latest statewide figures available. Hospitals say that vaccination rates for employees have increased in recent days ahead of the looming deadline, but they expect to lose at least a small percentage of their staffs once the mandate is in force.

Some hospitals are putting unvaccinated employees on unpaid leave for now, rather than firing them, in the hopes they will have a change of heart.

Gerald Cayer, chief executive of Lewis County Health System in Upstate New York, said his hospital would keep trying to persuade holdouts right up until Monday’s 11:59 p.m. deadline. About 20 hospital staffers were still unvaccinated as of Friday, while 43 had resigned because of the mandate. The resignations included half of the staff in the maternity unit, forcing the hospital to suspend baby deliveries beginning this past weekend.

“We’ve tried to encourage. We’ve tried to cajole. We’ve tried to give people space,” Cayer said. The compressed time frame between the announcement of the mandate and the deadline complicated the situation, he said.

“There is a lot of misinformation out there,” Cayer said. “When you are really trying to drive improvements in vaccination rates, five weeks is not a long time.”

Hospital workers have refused to get immunized for several reasons, administrators say, but most commonly because they do not believe the vaccines are safe or because they consider vaccine mandates a form of government overreach.

Some hospital executives said that they were taken by surprise by the number of staffers who declined to be vaccinated, even at the cost of their jobs. Tom Quatroche, chief executive of Erie County Medical Center Corp. in Buffalo, said he did not expect that 10 percent of the institution’s staff — about 400 people — would remain unvaccinated ahead of the deadline.

“The vaccine mandate was done for all the right reasons and with all the right intentions,” he said. “But the reality on the ground is that we’re not able to take care of patients appropriately.”

Ahead of the mandate deadline, the hospital suspended elective inpatient surgeries, paused certain transfers to its intensive care unit and reduced the hours at its clinics serving patients who are not admitted to the hospital. Some of the staffers who normally work in those settings are “putting on scrubs” to care for admitted patients, Quatroche said.

“The people who did get vaccinated and are facing this battle … I just couldn’t be more proud,” he said. But after 18 grueling months of treating patients during the pandemic, “this is just one more body blow for them.”

Hochul has refused to modify the mandate, delivering a consistent message that it is necessary and would not be delayed. On Sunday, she spoke at a church service wearing what has become a familiar accessory: a gold-colored necklace bearing the word “vaxed.” Hochul became governor in August after her predecessor, Andrew M. Cuomo (D), resigned amid a sexual harassment scandal.

New York’s vaccine mandate for health-care workers is still the subject of legal challenges. Earlier this month, a judge blocked the implementation of the requirement for people claiming a religious exemption, until at least Oct. 12.

Hochul said the state has prepared a plan to address staff shortages. On Monday, she said she would sign an executive order to give her the power to allow retirees or health-care personnel licensed in other states or countries to practice in New York, as well as to deploy members of the National Guard with medical training or federal personnel who normally respond to disaster situations.

Hospital executives have been racing to recruit replacements for unvaccinated personnel. Joe Ruffolo, chief executive of the Niagara Falls Memorial Medical Center, said that about 30 staff members had resigned because of the mandate and that he expected that a further 40 or 50 would remain unvaccinated ahead of the deadline. The hospital is relying more on temporary nurses from agencies while it recruits new staffers, Ruffolo said, and the cost of such staffing has skyrocketed.

“You’re paying some agencies more for nurses than you are for physicians,” he said.

Ruffolo said he believed the hospital would be able to weather the staff departures without curtailing services. “We should be able to skate by,” he said. But, he said, “we’ll have to make sure our skates are sharpened.”