Under the NHS, there are sometimes short wait lists for non-emergency operations. That's unfortunate and we are always trying to reduce the waiting times but, importantly, that surgery will get done in time and without any additional expense (or, if you have the cash, you can call up BUPA and skip the waiting time). And you're covered for everything. No lifetime cap, no cutting off of care. The only time the words "pre-existing condition" come up is when your doctor is checking that what he's about to prescribe you isn't going to aggravate something else you have and while your doctor might well ask a lot of questions, none of them are going to affect you right to care, he's just figuring out the best kind of care for you.
If you call your doctor, 95% of the time, you'll get an appointment that afternoon or, at worst, the following morning. If he prescribes you drugs, you take that to the pharmacy and you pay a small contribution (currently about $15) towards the cost of the drugs; the young, old and poor are exempt from that fee (I don't pay it because I'm on disability) and, if you need them for a prolonged period, there's various pre-payment discounts. Apart from that, your out of pocket expenses amount to the occasional roll of antacids or bottle of asprin. The doctor enters the details of your treatment into his records and every week, the details are transmitted to a central source which then reimburses him. Some doctors employ special software to speed up the process but that's not required, it's just something they do for their convienience and you can do the whole thing by hard copy although, obviously, it takes a bit longer.
I suffer from Type III Clinical Depression, known as Major Depressive Disorder in the States. It took me a long time to work up the nerve to tell my doctor how I was feeling (fear of disclosure is common to depression) and I had to be forced into it by my SO in the end. When I did explain how I was feeling, my doctor asked me a few questions, prescribed me some meds, personally booked an appointment with the local psychiatrist and ordered me to come back and see him every week. I waited three weeks to see the psychiatrist. I now take 225mg of Effexor and 10mg of Zyprexa daily (actually, generic equivelents, plus 15mg Lansaprozole for a completely unrelated stomach condition), see my doctor every two weeks and my psychiatrist every two weeks (carefully arranged so I never go longer than a week without seeing one of them) and I'm gradually doing a little better. I'm still self-harming but not as often or as badly. All of this support costs me nothing, just the taxes I've already paid and the taxi fare it cost to get to the doctor that first time (I have a fear of public transport). Subsequent trips to the doctor or psychiatrist are subsidised.
Here, the average tax rate is 22% (plus 8-9% National Insurance, our version of Social Security). Part of that supports the NHS. Now, I'll be the first to admit that the NHS isn't perfect. It's difficult to think of anything that could be but let me tell you about the NHS. The annual operating budget is a shade over $2000 dollars per citizen (around 60 million citizens) per year. Most of that comes from taxes but some comes from indirect taxes. For example, I smoke. A pack of Marlboros (my preferred straight, I normally smoke roll-ups) costs about £5.50 here. Of that, about £4.50 goes to the NHS to pay for treating smoking related illness. And I'm fine with paying that. I have a habit which could be damaging to my health so I pay a bit extra to cover the cost of treating my health. Seems perfectly fair to me. There's a tax of a couple of pence on a pint of beer or about a pound on a bottle of spirits for much the same reasons. With junk food, it's easier to tax the corporate profits but they chuck a bit into the kitty as well. It's important to point out that care isn't cut off if you go over that $2000 budget or the NHS exhausts it's funds, that happens sometimes. The budgeting office of the NHS just goes to the government and says "we need this much more" and they get it. The budget is just used to give a rough idea of where the "sin taxes" (the ones on alcohol, tobacco, junk food, etc) should be set next year.
Try finding a private insurance plan that covers you for everything for that price. Extrapolating up, the annual cost to run a USHS (for lack of a better term) would be around $600 billion a year, not counting start-up costs. Perhaps you want to go the French route, usually ranked as the world's best system? That brings the price up to $900 billion. Sounds expensive but not when you consider that the combined costs of Medicare, Medicaid and private insurance is $2.3 trillion and a combined system would replace all three. Nor do you need to limit yourselves to those two systems. Other nations have different methods of administering and paying for their healthcare systems. You could easily set up a short-term committee to study the existing systems and then mix-and-match parts, taking the delivery model from this one and the funding structure from that one (for example, we tried on-the-day-only appointments here for a while. Doesn't work), until you come up with something special and uniquely American.