It's a very similar system, the real difference is that it's illegal to not have insurance, so you are "forced" to always be insured, and unemployment support is more generous.
This sounds more like a hypothecated tax.
American government is a uniquely incompetent form of government. Despite being one of the largest & most expensive governments it gets little to nothing done. Anything that is 'done' is often done far over the original projected budget.
Objectively untrue by any serious metric you'd like to go for, and in particular government-run health insurance programs (Medicare chief among them, but also the VA) are notably well-run and have low incidence of fraud while maintaining remarkably low overhead.