All veterans and their spouses are eligible to get vaccinated for the novel coronavirus (COVID-19) through the Department of Veterans Affairs, and based on multiple first-hand accounts from veterans, many of them are getting same-week appointments.  You don’t even need to be enrolled in the VA to get signed up for a vaccine

COVID-19 vaccinations at the VA are available to the following groups:

• Spouses of veterans. In other words “If they characterize their relationship as spousal, they can receive the vaccine at VA,” said Veterans Affairs spokesman Randal Noller.
• Veterans who are eligible for hospital care, medical services, and nursing home care abroad.
• Family caregivers approved under the VA’s Program of Comprehensive Assistance for Family Caregivers.
• Caregivers of veterans participating in the VA’s Program of General Caregiver Support Services. 
• Caregivers of veterans participating in the VA’s Medical Foster Home Program, Bowel and Bladder Program, Home Based Primary Care Program, or Veteran Directed Care Program.
• As well as Civilian Health and Medical Programs of the Department of Veterans Affairs (CHAMPVA) recipients, a health care program in which the VA shares the cost of covered health care services with eligible beneficiaries.

Source: Task& Purpose by James Clark April 06, 2021