Up to 12,000 Air Force personnel have rejected federal orders to get fully vaccinated against the coronavirus despite the Pentagon mandate, and officials say it is too late for them to do so by the Tuesday deadline, posing the first major test for military leaders whose August directive has been met with defiance among a segment of the force.

The vast majority of active-duty airmen, more than 96 percent, are at least partially vaccinated, according to data from the Air Force. But officials have warned that, barring an approved medical or religious exemption, those who defy lawful orders to be fully immunized are subject to punishment, including possible dismissal from the service, or they could face possible charges from within the military justice system.

The challenge now facing Air Force leaders — how to address potential major dissent in the face of a top health priority which has been deeply politicized — is a bellwether for the dilemma in store across other service branches, which all have compliance deadlines ranging from the end of November to the middle of next summer and, in some cases, have seen far greater resistance to President Biden’s mandate.

A wave of dismissals could jolt the Air Force personnel system and cause significant challenges within units that must be ready to respond to crises at a moment’s notice, especially if some vital jobs — like pilots or aircraft maintainers — are overrepresented among those who could face expulsion, said Katherine Kuzminski, a military policy expert with the Washington think tank Center for a New American Security. “The fact that it’s a choice leading to potential loss to readiness is striking,” she said.

The Air Force is the third-largest military service, just behind the Navy, with 324,000 active-duty airmen, making even 3 percent of its ranks a substantial figure. For comparison, the personnel assigned to Nellis Air Force Base in Nevada, one of the service’s most-populated installations in the United States, numbered slightly over 10,000 in 2019.

The Air Force declined to say how many airmen appear to be outright refusing vaccination versus how many are seeking exemptions or have opted out since they are close to their scheduled exits from the military. The Air Force will release some of the details after next week’s deadline passes, said Ann Stefanek, a spokesperson for the service.

Pentagon spokesperson John Kirby has said that, generally, the number of religious exemptions for any vaccine is “very small.” The Army, the largest military service, has granted just one permanent medical exemption and no religious exemptions for the coronavirus vaccine, officials said. The Navy hasn’t granted any religious exemptions for any medical vaccine — for the coronavirus or otherwise — in the past seven years.

The religious objections have centered on the fetal cell lines used in some aspects of vaccine development, essentially reproductions of cells out of abortions performed in the 1970s and 1980s. The shots themselves don’t contain the actual cells. A regimen of numerous vaccines is required upon joining the military and even more if troops are deployed overseas. Some of those required vaccines, including those against Rubella, chickenpox and hepatitis A, also were developed using similar cells.

Vaccination rates within the Air Force have slowed in recent weeks, and it is too late to now begin a regimen and be in by compliance by the Tuesday deadline, indicating that the Air Force has mostly immunized all service members who want to get the vaccine, officials said.

Airmen receive counseling from leaders and medical providers when filing a medical exemption from the vaccine mandate. For a religious exemption request, service members must meet with a chaplain to determine if their request was generated by a “sincerely held belief,” Stefanek said.

Information about their request is forwarded to a senior commander for consideration, she said, typically a three-star or four-star general who must weigh an individual’s request against the unit’s mission needs.

Even if the commander believes an airman has made a sincere request, it may be denied if it is believed the unvaccinated airman could harm unit cohesion or make it too difficult to work close together, she said.

Historically, most administrative exceptions have been made for service members who are near a previously planned departure, she said. Airmen who secured approved retirement or separation by Nov. 1, with an exit by April 1, will not be subject to the vaccine mandate, Stefanek said.

Overall, the military vaccination rate has increased since August, when Defense Department leaders informed the 2.1 million service members of the United States that immunization would become mandatory.

Nearly 87 percent of active duty troops are fully vaccinated, Kirby said, though hesitancy among military reservists and National Guard members drives down the rate for the entire force to 68 percent. The numbers vary widely between service branches, fueled in part by the differing deadlines and cultural reasons, The Washington Post found.

As vaccination rates rose, so did military deaths attributed to the more infectious delta variant, with 71 coronavirus-related fatalities in the ranks to date. In September, more military personnel died from coronavirus infections than in all of 2020. None who died had been fully vaccinated, according to Pentagon spokesman Charlie Dietz.

Service members who decline to get vaccinated face an array of potential discipline. The Air Force has said airmen who refuse can change their mind after speaking with their commanders or if their request is denied, though further noncompliance faces an escalating set of punishments, including involuntary separation or court-martial charges.

Similar violations could be handled differently in the other services, which Rachel Van Landingham, a former Air Force lawyer and president of the National Institute of Military Justice, deemed unfair.

Defense Secretary Lloyd Austin can and should impose one standard of accountability, removing the commanders from the process and limiting punishment to administrative discharges, rather than sending decisions to military courts, she said. Austin will likely not do that, she said, since the services “are parochial and don’t want to give up power.”

Nearly 40 recruits in the Air Force training pipeline were recently forced out of the service for declining to get vaccinated, officials said. They were sent home using a discharge method to easily banish recruits who fail to meet standards before officially entering the military.

Airmen who decide to leave the military over the vaccine mandate may face similar retention problems if they want to transition to federal government employment or jobs with government contractors, which are popular draws for veterans but now mandate the immunization as well.

Michelle Boorstein contributed to this report.