The problem with Obamacare is the mandate.
However, if we are going to be honest with ourselves as a nation, you will not be able to create a national healthcare system and use private insurance companies without the mandate.
You have to have the young people who never get sick, forced to pay for it, so that those who do get sick, can be covered.
There is no other mechanism to do so other than single payer healthcare systems and that is always going to be called "socialist".
You can't have it both ways. People just don't want to admit it.
It's easy to pull an Ivan Drago and say "If they die, they die.", but we believe ourselves as a nation to be "better" than that.