Yes, when you tie two things together, walking away from one usually entails walking away from the other.
Your clever observation is a symptom of a deeper malady.
Our economic system (capitalism) has been at war with our constitution for some time, bending it like a pretzel.
Care to declare a winner - or is a peaceful solution attainable?
I would say that's more a huge issue with the US politics. In most of Europe you don't need to worry about health insurance at all; everyone has it - regardless if you have a job or not.
It's the GOPs FUD agenda that anything in governmental control is a step towards communism which plays out here. In addition to their greed agenda ("I don't want my tax money to sponsor other people! It should only benefit me.").
And since the US political system isn't a true democracy; it's corporatism - where it's companies funding politicians ... This won't change at all. Since the corporations can help exclude politicians working to reduce the corporate impact on the politics - simply by funding politicians supporting them instead.