Cheap health care, just around the corner!

So I hear universal health care is going to save us tons, I'm not sure how... but I really would like to know. Basically, it seems like there will be some big fund that will pay for health care or health insurance. Who will run this fund is unclear, the government "doesn't want to, really" (the way they don't want to run GM or the banks I suspect), so it may be some semi-private freddie mac type outfit (that went well). But what IS clear is, the money will come from (us)... since the government has only that one source.

So my real question is, how does this set up make sense, in a cost saving way, given these facts-1. Everyone needs health care, and from person to person it will cost about the same, that is if health care becomes truly universal.
2. Since everyone needs health care, it seems like everyone should "chip in" to this fund, though obviously some will "be able" to chip in more than others.
3. Since this money (that we all chip in) could have & probably would have, gone towards health care, if not for the new system... It now has to fund health care, as well as funding the new agency/org. that will run the fund.

What would this new outfit cost? I have not even looked to see if someone has an estimate, since the dems will lie to the low side by Powers of ten & the same in the other direction for the republicans. So I thought about it & figured an organization like what would be needed would be a lot like the IRS... collecting taxes ("contributions"), deciding who can pay what... catching cheaters... etc. I guess it might take a little bigger org. since it will also have to deal with health care providers on the other end, so I will add 50% for that.

The IRS will cost us around 11.4 billion this year, so add 50%, you get close to 17.14 billion. Then you have to factor in that, people are already insured... so to get the fund going, money will have to be borrowed... so it will start off in debt, massively. Just figure it will need a trillion to get in rolling, 100% financed, since there is obviously no extra money laying around. Say the interest rate is 5%, the fund will start off, before it does a thing, owing 50 billion a year, just to service the debt. So for the first year, not counting the principal, the savings (whatever it is) will cost us 67.14 billionish... That's $225 per person, for every man/woman/child. Family of 4, $900 a year.

I just cant see any other way of looking at this... a massive agency will cost a LOT, it just will. Borrow the money & let future generations deal with it? Seems like a dick move, number one... But I'm not even sure we can, we are just so in debt now, countries we borrow from are getting nervous.

But really, if someone knows where the savings come from, let me know... I cant find it.