Senpai's response is pretty typical of what you'll get if you try to discuss this with an American.
"How do we expect us to pay for it?" Well, the answer to that is "with the huge amount of money you spend on an inefficient healthcare system already".
UK healthcare spending as a % of GDP: 9%
US healthcare spending as a % of GDP: 17%
The Americans spend roughly twice as much on healthcare for a system that leaves substantial numbers of people uninsured.
You're cute. Us poor Murican's just have no clue what we're talking about. This is the typical response you'll get if you try to explain it to a Brit who has no fucking clue how our economy works. 
That's all true on the percentage of money spent per person. But you're leaving out the fact that our medical procedures cost much more than yours, the fact that we regularly provide medical care to people who are illegal and uninsured, and the fact that what we cover per person is the people who are uninsured.
Right now we spend 17% on people who are uninsured. That's only 15% of the population, everyone else pays for themselves. Most insurance is subsidized by the company, meaning they pay less because the company purchases large group packages. Some pay more, some pay less depending on overall health.
So let me break it down for you again.
We are currently paying 17% on 15% of the population. Tell me, then. How do propose we keep those pesky tax numbers numbers down when:
- We would have an extra 85% of the population to pay for.
- We no longer have companies helping to subsidize insurance rates.
- Our medical companies are not going to budge on prices.
- We're all on the same package and can't choose the less expensive option
- Our hospitals are already declaring bankruptcy as it is because our gov isn't reimbursing them for the uninsured they treat like they're suppose to.
Taxes will go up for everyone to cover the cost, and the people that will be hit the hardest is the middle class who already are taxed the higher than any other income bracket in relation to their salary as it is. It's just going to effectively shrink our already shrinking middle class.
Your idea is great in theory. The only good thing this program has done is keep the scummy insurance companies honest and prices down so people go to them instead of gov. insurance.