I hear this several times a day, so I thought that I would, as I often do, supply you with the correct information.
The Patient Protection and Affordable Care Act, often called the Affordable Care Act or Obamacare, does not actually issue people any insurance. It expanded public and private insurance access. Applicants either sign up for Medicare or for one of the many private insurance companies. Many people have gone around the exchanges and simply applied directly on the insurance company websites. There is no “Obamacare Insurance.”
Also, the idea that the government cannot compel someone to do something is simply an Arguement From Ignorance.
As a simple example, take the Selective Service Act. Since 1917, American and non-US males are forced to register with the government within 30 days of their 18th birthday for potential government service. The current penalties are up to 5 years in prison and $250,000 fine. Most federal benefits are permanently barred, and all but 8 states also deny services. There are no exceptions allowed to registration. In 1987, a separate system for drafting male and female health workers was established. Unknown to most citizens, most states also have their own separate draft systems established for their own purposes, taking the information from the Federal Selective Service lists.
So, there is no Obamacare Insurance and yes the government can force you to do things you don’t want to.