Not normally.
How to cancel an Obamacare health planYou don't have to keep it until the end of the year
Go to the health insurance marketplace where you bought the plan and sign into your account. If you bought it through HealthCare.gov, log into My Account, go to My Plans and Programs, and select End/Terminate All Coverage.
Youll need to pick a termination date thats at least 14 days in the future, presumably to give the marketplace and your insurance company time to process your request. Needless to say, double-check when your new health plan starts so you dont end up with a coverage gap.
If you bought through a marketplace run by an individual state, the termination option might look different than it does on HealthCare.gov. If you cant find it at all, call the customer-service line instead.
I did have the number who have cancelled in my state but can't find it now.
If all else fails, just rent a PO box in another state and tell them you moved there. It will be cancelled pronto.
Most. Stupid. Administration. Ever.