After you leave your job, by law you have 60 days to elect COBRA health insurance continuation coverage. COBRA insurance is usually much more expensive than your monthly premiums because you are also paying your previous employer’s share.
If you are generally healthy and are worried about the cost and do not plan on keeping COBRA insurance for more than 2 months anyway, wait the 60 days. If you end up not using COBRA, you can let the 60 day election window expire, and explore your other options. But if you end up do needing medical care, any election during those 60 days is retrospective for the entire 60 day period.
But be aware that if you are planning to continue insurance through a spouse or the ACA marketplace, you may only have a 30-60 day special qualifying event window to elect the new insurance. Other options exist, such as buying short-term health insurance or applying for Medicaid (if you are eligible).
The cost of COBRA coverage is usually very high. You can ask HR for the cost of your COBRA plan. Otherwise, part-time employees generally pay the full price of health insurance without any subsidy from their company, so you can estimate your cost by looking up how much they are paying.
