"OK, but those other countries all have shitty public insurance, whereas America has private insurers paying for a lot of the costs." Well, America does spend a lot of money in the private sector on health, but even public spending per capita is third highest, behind Norway and the Netherlands. In short, your taxes are already funding a massive public health system, whether you realize it or not.
So where's that money going, and how can it be more effectively used? Those are huge questions that probably aren't going to be solved while reading on your phone, but one problem area is pharmaceuticals: America spends way more on them -- partially because we don't allow Medicare to negotiate prices -- than other countries with large public health systems. Instead, private insurers do the job, and they are, after all, for-profit companies that have the bottom line, rather than health outcomes, as the primary objective. Those profits are considerable -- even with insurers griping about losses they're taking by participating in Obamacare exchange plans, they're still doing OK, with UnitedHealthcare reporting profits (again, profits, not revenue) of just under $1billion in the third quarter of 2015. Imagine what could be done with just some of that money!