So Scalia agreed that you're allowed to burn a flag in America. That's great -- but how did this ever even become a Supreme Court case? If you burn a flag in Sweden or France, nobody would think to sue you. The fact that this freedom had to be weighed at the highest possible level shows that Americans have serious blind points around their perception of freedom. Similarly, European countries have individual historical taboos on speech, such as the ban on Nazi symbols in Germany.
In the US healthcare debate, the right's constitutional argument seems to revolve around Obamacare's individual mandate -- but that's just is a clumsy artifact of how the system was overlaid on existing pseudo-private healthcare systems. With a properly designed tax-funded public healthcare system, the problem would go away.
In the healthcare debate, the American right argued that the national government didn't (and shouldn't) have the power to take certain steps. The European right mostly argues from practical or identity-based reasons. So healthcare controversies involve levels of funding, pay for workers, coverage for refugees, and things like that.