What will the Affordable Care Act mean for the unemployed? How will it affect COBRA coverage? Being laid off is difficult. With COBRA, you can choose the health insurance coverage you need for a time period based on whether you or a spouse needs Medicare and if you have children on your health insurance plan. The time period ranges from 18 months to 36 months. You can usually elect to continue coverage for anything covered prior to unemployment. Learn more about COBRA health insurance coverage here.