At Mass General Brigham, the state’s largest hospital system, more than 95 percent of employees have been vaccinated. But about 4,000 workers have yet to receive their shots or provide proof of vaccination ahead of the system’s Oct. 15 deadline.

RosemarySheehan, chief human resources officer, acknowledged that some of those employees will lose their jobs. “I’m hoping that it’s in the hundreds and not close to a thousand,” she said.

Hospitals in Massachusetts and many parts of the country are requiring employees to get their shots to protect patients and co-workers from the spread of the virus, and to help bring an end to the pandemic.

The vast majority of health care workers rolled up their sleeves when vaccines became available, but a small fraction are so opposed that they’re willing to lose their jobs.

In Rhode Island last week, more than 300 people protested at the State House in support of health care workers who had refused to comply with the state’s vaccine mandate.

In New York and California, statewide mandates for health care workers appear to have increased vaccination rates.Northwell Health, New York’s largest health care provider, said this week that 1,400 of its employees left their jobs over the requirement, less than 2 percent of Northwell’s workforce. Overall, the number of health care workers leaving their jobs over the vaccine in New York is not causing the kind of shortages some had feared, The New York Times reported.

Massachusettshospital leaders said that they don’t want to have to fire anyone, but that if employees refuse an effective vaccine to protect themselves and others, they should not be working in an industry that is rooted in science and treats vulnerable people.

“This is a very difficult time for everyone, and we’re trying to respond with what’s best for our patients,” Sheehan said. “That has been the beacon that has driven all of our decisions.”

At Beth Israel Lahey Health, 91 percent of the workforce has been vaccinated, but about 3,000 employees have yet to comply with the requirement to get inoculatedby Oct. 31. Dr. Kevin Tabb, chief executive, said he expects most will get shots by the end of the month, but as many as a few hundred could lose their jobs.

“The vast majority are not refusing outright to get vaccinated,” Tabb said. “There’s been hesitation, and we’re overcoming it.”

Beth Israel Lahey Health is among the Massachusetts hospital systems developing contingency plans — including reshuffling staff and increasing hiring — in case it has to fire large numbers of employees.

“We aren’t currently contemplating cutting any services,” Tabb said. “We don’t think the addition of . . . a small number of employees who choose not to get vaccinated will tip that balance. The larger challenge for us is the large number of open positions that we and other health care systems have — unrelated to vaccination.”

UMass Memorial Health Care is giving employees until Nov. 1 to get shots. So far, about 90 percent have been vaccinated. If “we have to let go of unvaccinated workers, that unfortunately will impact our ability to provide the care and services to the people of our region,” spokesman Tony Berry said. “We will do everything we can to not have to resort to program closures, but . . we may have no other choice.”

Boston Medical Center employees have until Oct. 15 to get one dose of vaccine, and so far, 90 percent of the 9,500 workers have done so.

The total number of Massachusetts hospital workers who lose their jobs over vaccination mandates won’t become clear for weeks. Many hospitals are putting workers on unpaid leave and giving them a grace period to get vaccinated before terminating their employment.

Workers can ask for medical or religious exemptions, but hospitals rarely are granting them.

Workers who resign or are fired from hospital jobs after declining the vaccine will have limited options if they want to continue working in health care. COVID vaccination is almost universally required for workers at Massachusetts health care facilities — and now alsoat many employers outside the health care field.

At the Wellforce hospital system, which includes Tufts Medical Center, 97.5 percent of employees were vaccinated by the Oct. 1 deadline. About 325 people have not received the shots. Wellforce spokeswoman Brooke Hynes said it’s too soon to know how many will ultimately lose their jobs.

“It’s a challenging market, and so you never want to lose anyone, but we have to have the safest environment for our patients,” Hynessaid. “We feel that’s what they depend on us for.”

The experience at some hospitals whose vaccination deadlines have passed shows that near-universal compliance is possible.

Among the Dana-Farber Cancer Institute’s workforce, 99.4 percent have been vaccinated, while 54 people have been suspended without pay for declining the vaccine. They have two weeks to begin their vaccinations or leave their jobs.

“Mandates send the right message about the critical importance of vaccination to control the pandemic, and they produce real results,” said Dr. Craig Bunnell, chief medical officer.

The fact that Dana-Farber specializes in treating immunocompromised patients who are at higher risk of becoming ill from COVID likely convinced employees to get the shots, Bunnell said. “We have a singular focus on cancer, and our patients are among the most vulnerable individuals in society,” he said.

More than 99 percent of the workforce at Springfield-based Baystate Health also received their shots by the Oct. 1 deadline, while 145 people were placed on leave and have two weeks to get vaccinated “if they wish to continue their employment,” Baystate officials said.

In Massachusetts, the next few weeks will be critical for getting health care workers vaccinated. The state did not mandate vaccination for all of them, but nearly all hospitals agreed to require the vaccine for their employees, setting deadlines in October and November. The Baker administration also mandated vaccination for long-term-care and home-care workers.

“Right now the push is really education,” said Sheehan of Mass General Brigham, noting the health system is providing information online, on paper, and through one-on-one conversations with employees.

“I’m cautiously optimistic,” she said. “The numbers improve every day. Like anything else, a small portion of the population is going to wait until the last minute.”