As far as the health care debate in the US, I don't live there, and it doesn't directly effect me, so I don't much care. There are other laws in the US that are a higher priority to me to change. I think there are lots of systems in the world that are working much better than the US system, and I don't understand why you'se don't just take some of those ideas and run with them.
General Organisation
In the US, providers are private. Each is in business, and they charge per service that they provide. To help people cope with high costs of many services (particularly catastrophic illness or injury), health insurance companies exist. They are regulated, but determine who they insure, and can charge based on almost anything they want.
In Australia, providers are also private. The only exception to this is hospitals, some of which are private and some of which are public. Each is in business, and they charge for services that they provide. They determine what they want to charge, and compete for patients based on cost, quality, etc.
The government has a program called Medicare, which pays a pre-determined amount for various procedures/consultations/services. The amounts are revised periodically. Some providers charge above what Medicare pays (called the scheduled amount), while some decide that they'd rather have the higher amount of patients, and they heavily advertise that they "bulk bill" which means they don't even bother billing you for the procedure, they simply send the bill to Medicare and get reimbursed from the government.
As I mentioned earlier, there are two kinds of hospitals, public and private. Public hospitals are paid for by the state government and going there is either free, or very very low cost. The trade off is, of course, waiting times. For non-life-threatening procedures, waiting times can be up to a year. If your condition is life-threatening, you get top notch care immediately.
Private hospitals are paid for outside of the public system. You have the option of purchasing private health insurance. This insurance operates in conjunction with your Medicare (NOT instead of), and pays for extras like optical and dental, as well as stays in private hospitals. Because they're competing with free, they often give you lots of extras, including private rooms, longer monitoring periods before they discharge you, short to non-existent waiting periods, and they try to provide "better" care.
Private Health Insurance
Private health coverage steps in when Medicare doesn't, covering you in private hospitals, and covering extras. Most private heath insurance companies require you wait various periods before you can claim different extras.
An interesting difference is the difference between an excess and a deductible. Here, you can elect to pay an excess to reduce your premiums, but this excess only kicks in when you get admitted to a private hospital, not for any of your extras. My current excess is $200, and I pay $105.10 per month. This also includes $100 per year in an account I can use to pay medical expenses of any kind.
Immigration
Medicare is paid for by taxes, so what about people that have just moved to the country? How do we make it fair to prevent people coming in and mooching off of the system?
If you're here on a temporary visa, you do not get Medicare. You are supposed to purchase Medicare equivalent insurance. This is insurance that pays the same as (and possibly more than) Medicare. Once you are granted a permanent visa (like a green card), you become eligible for Medicare.
Cost
One of the most important factors in healthcare is how much it costs you. I'm no expert. My personal experience is that it's much much cheaper here. Taxes are higher though, so does it even out?
Here's a pretty picture:
Total Health Expenditures Per Capita, U.S. and Selected Countries, 2003

Well, I guess it's not pretty if you live in the US.
That was sourced from the Kaiser Family Foundation. I have no idea what their bias is, nor do I claim it's objective. I simply don't know enough about the statistics. Feel free to do your own research. Here's where it came from: http://www.kff.org/insurance/snapshot/chcm010307oth.cfm
So, I can't really comment much more on price other than my own experiences, which I've added at the bottom.
Pre Existing Conditions
Because I have a pre-existing condition, when I first rang up the insurance company here, I was nervous. How much would they charge me? They asked me my birth date, name, address, sex, and credit card details. Voila, I had health insurance. Turns out that in Australia, it's actually illegal to charge people more based on any sort of health condition. They can charge more based on sex and age, but can't ask you about your medical history. I think at the very least, the US needs this.
A Few Examples
These are a few personal examples I have of interactions with the Aussie health care system.
Skin Tag
I had a particularly annoying skin tag on my back that I wanted to get removed. I went to the medical centre, gave them my details, and ended up waiting about a half hour with no appointment. The doctor gave me anaesthetic, cut it off, and then cauterised the wound. I signed a piece of paper on the way out, and left. Medicare was billed $34 for a consultation, and $86 for the removal of the actual skin tag.
Sleep Doctor Appointments
I needed to be referred to a sleep doctor, so I went down to the medical centre. They gave me a referral. Medicare paid $34 for a consultation.
I then had my appointment with the sleep doctor. This doctor does not bulk bill, and charged me $180 for the appointment out of pocket. After the appointment, I went to Medicare and made a claim. The Medicare scheduled rate for a specialist appointment was $111 roughly, and I received that in cash from Medicare.
Catastrophic Care
My partner's father had a stroke. He was brought to a public hospital by an ambulance and triaged in the ER. He received a drug to thin his blood along with the usual ER care. When he came to, he could not move the left side of his body. He spent around 2 weeks (I don't remember the exact amount of time) in the hospital recovering and going through therapy, and then spent a further 4 weeks in monitored care where he got physical therapy attempting to help him learn to grab, chew, swallow, speak, and generally live again.
He received all medications that he needed, lots of specialist care, and has recovered completely. Total cost, $0.
Optical
I wear glasses. Eye tests are covered by Medicare (one per year), so the test was free. I then chose a set of frames, and got middle of the road lenses. Total cost for frames + lenses was around $350. My private health insurance with optical extras kicked in and I needed to pay $70.
Side note: Medicare apparently will get you glasses if you need them, but they're the ugliest possible black frames.
Lap Band
I have a friend that had recently got a lap band. She did have private health cover, but because it's not medically necessary, she still ended up paying around $5,500 for the procedure out of pocket. If she didn't have private cover, she could have gone public, but there would have been a wait time of over a year, and it would cost around $8,000.
Overall
Personally, I prefer Australia's system. It's not perfect. Particularly people from the US tend to complain that it's hard to get in to see a specific GP, as in you don't have that trusted family doctor that knows everything about you. Most people here go to a medical centre and get appointments with a particular doctor, but if that doctor is busy or not in when they come in without an appointment, someone else will see them and take care of them.
Also, dental cover is a big hole in the system here that is widely acknowledged. I just purchase private cover, and my dental cover is fine, but if you were poor, this wouldn't be an option.
Finally, there is the concept of a Medicare Levy. This is an additional tax that people pay if they're over 30, make a certain amount of money, and don't have a basic private health cover. This is an attempt to move some of the burden off of the public system and also to subsidise the private system to ensure there are options out there. Personally, I see no issue with it.
I think if you have lots of money, the US system is probably better for you. You'd have amazing insurance and be able to get (basically) whatever you want. For me, I'm bloody happy that I have a place I can go for the rest of my life where I'll be able to get medical care at sane prices.