The best faith argument against health care for all is that it creates a strong incentive to limit freedom.
If the government were responsible for everyone's healthcare, then it would want to reduce healthcare costs. If it were to reduce healthcare costs, it would have to understand and regulate or tax things that hurt health. Things that hurt health are things like sugar, tobacco, alcohol, advertising unhealthy stuff to children, sports, especially adventure sports, driving, etc.
If the government can draw a direct correlation between sugar consumption and health costs, there is now a strong incentive to tax and regulate sugar.
If people go skiing and that becomes a significant health cost (broken bones) you now have a strong incentive to tax skiing.
For adventure sports, it's easy to imagine what is currently the balance between safety and excitement could end up being regulated past a point you would personally be happy with.
This increases government size, increases government intervention, and limits both business "freedom" and individual freedom. The catch phrase for this line of thinking is "nanny state."
Personally, I don't like being obese, and I don't like looking at obese people and "just don't eat sugar" is harder than it sounds. I am quite in favor of government intervention for the benefit of society as a whole in the form of things like sugar tax or sugar regulation, but I find the argument that this kind of intervention harms freedom compelling (just not more compelling than the benefits of giving up that freedom).