Tips for getting a health plan ahead of Tuesday's Open Enrollment deadline Christopher Furlong/Getty Images Posted at 9:30 AM, Dec 15, 2020 and last updated 2020-12-15 11:22:09-05 (WXYZ) â The deadline for the Open Enrollment Period is Tuesday and those looking to get a health plan through the federal government or private insurance will need to enroll before midnight to get health insurance for next year. Priority Health has several tips for those who are looking to enroll. First, the healthcare provider said to think carefully about what you or your family needs. Things to think about include plans for specific prescription drugs, a possible life change, any surgeries and more.