@JY, ok, i know you're analyzing the issue from a positive/negative rights pov and a individual vs states vs federal responsibilities/powers pov.
But there are other ways of looking at the world, and i think being able to see things from different perspectives is useful to complement our understanding. So i will advance one.
The Marxist analysis, which will necessarily be based on class - because though many other theory have been built on his ideas of conflict within society, like feminism, anti-colonialism/anti-rascism, and the queer rights movement - Marx was limited to seeing things through the lens of class.
From this perspective, the state is an institution of power, a manifestation of the interests of the powerful. Mainly the ruling classes. And the working classes are required to serve and pay for state functions.
There is a fair arguement to say the the US has more social mobility than the Germany/Prussia which Marx was writing about; but it is still a given that the division between employer and employee exists in the US. That 'tax breaks for the rich' because they are the 'job creators' is still an idea because the rich and powerful still act as a ruling class (it is possible to imagine a society where corporations are democratic, and individual workers have a say in executive level decisions, but this is not the case, so i will continue with the Marxist analysis for now - despite acknowledging it has weaknesses).
From this perspective, the wealthy and powerful have healthcare and the poor working classes do not. It is a clear divide - even if there are shades of grey, with various levels of coverage, different co-pay options, and costs - but in simplified terms, there are those who can afford good healthcare and those who fear being bankrupted by illness.
In this analysis the working poor, and unemployed must fight to maintain their current entitlements, and to expand them. Now Marx would likely go on to claim that revolution was inevitable, and that the people will rise up in solidarity to claim what they are entitled to... but of course Marx continues to have been very bad at predicting the future (which is a pity because his analysis of what was true remains pretty good).
You've seen US workers fight for the right to employers paying for health insurance. And there is nothing, in this view, which alters the 'right' or 'wrong' of this fight from a fight to generalise to all citizens receiving health insurance/healthcare - though i know Marx would be upset at the idea of individual unions fighting for rights for their members only... the democrats in the ACA attempted to do a little bit better than Unionized workers managed in the 30s.
Now, for your perspective, sure, there is a difference - between the collective bargaining of a Union with the Industry leaders. That is a private agreement between two negotiating parties. While the people coming to a compromise among themselves to provide healthcare for all citizens is clearly some violation of property rights... Oh wait, it is only something you could oppose if (in the Marxist view) you are one of the wealthy members of the ruling class.
Of course "the people coming to a compromise" is exactly what is supposed to happen if your republic is democratic. Except in my view (influenced by Marx) the power has shifted away from the people and into the hands of the few lobbying corporations and deep state powers concerned with national security.
As with all ideological perspectives, there are flaws and limitations to the Marxist view, but no more so than any other perspective.