Cash for Clunkers is a great example of a government program. Some facts:

• When it started, each dealer was faxed a 187 page document detailing the restrictions on what they would take for a car. 
• They think they are out of money, but they have no clue, because they didn't expect the number of people who would use the program to be so high, so they under staffed it.
• The dealer I just bought a Jeep from, has 15 cars that the government has yet to decide on if they will pay him for.
• In one week, they have tripled the cost of the program.

Now, this is the same people who will be running your healthcare.

Scared yet?

I like the way you put this...but just to give you more prospective...
Look at social security, I do not expect to get a dime from it when I turn 75 or whatever the age will adjust to in 43 years.
Look at the DMV. How many times have you stood in line for an hour just to have some idiot who doesn't give a crap, give you two little stickers to put on your license plate.
Look at the school systems, churning out socially inept morons
Look at the Medicare/Medicaid system, Bankrupting hospitals and seniors at the same time, while not paying for much needed health care proceedures.

Lets see:

The last time I went to get my car license it took me all of 60 secs to get done: Public entity. The time before that it took 3 minutes and the time before that it took about 4 minutes. I do it every 6 months or so.

The problem in America is not the government doing things, its the fact that your government does so many things badly. The DMV is just a really good example.

Btw, the same kind of people running our socialised health care are the same people running the licensing of cars in that they are public servants.

If the proposed government healthcare plan, was to have New Zealand run it, I would be less scared.

The reality is our government does run things badly. Why then intrust them with something this important to run?

I would say quickly as im heading off to bed is probably down to 3 important factors that I can think of:

1. The U.S. government is full of conflicts of interest between politics and corporations/other interested parties (lobbies) (re-election money), conflicts between State and Federal government levels (State pork, I.E put this lil project on this and I'll give you my vote).

2. Government departments are run on the 'spend it or lose it philosphy' so waste is built right into the system when your budget next year depends on how much you spend this year.

3. A corporate model of accountability can be applied to a government department as easily as it can to a corporation. Many of our 'State owned' functions like healthcare, post, power production are run on a corporate model and are actually very efficient. Our postal service returns a profit to the government every year for example.

To solve it my best guess would be something like this:

1. Return powers back to the states as governments are a lot more efficient spending their own taxpayers money and not so much when it comes out of a bottomless barrel.

2. Corporatise government departments, hire outside executives and run them like a business with bonuses etc set on achieving performance targets if neccessary.

3. Give candidates with a set proportion of 'pre-votes' a substantial quantity of money so they can run fairly with better paid candidates to ensure its the best person who got the election win and not just the person with the most money.

I think it's ridiculous to take one very badly run program and use that as a reason not to have universal healthcare.

Do you think that policing, prisons, education, judiciary, and everything else should be taken out of the hands of the government as well and moved to the private sector?

Umm... you forgot to name a federal program. All of those are state run. (aside from a small percent of judiciary).

I think the 'Cash for Clunkers' program, and several other programs started since the beginning of the year, should be more of a concern for people when it comes to the healthcare reform bill because it demonstrates an inability by the current government to accurately project costs and the effects their programs will have. Consider (for a moment) that the government over-estimates their ability to reduce costs and fund the system through taxes by 50%, and underestimates the cost associated with running the system by 50%, you will end up with a system that costs $900 Billion where you have only paid for $400 Billion and you add $500 Billion to a $2 Trillion deficit.

And please name a program that is both run by the private sector and the government, and the government does a better job.

Private education is far better, and far cheeper.

Private healthcare is far better, and far cheeper.

Private roads are better and cheeper then public roads.

Contracted security forces are better and cheeper then government ones (it's why the military contracts them).

Private manufacturing is far better and cheeper then government. It's why our military buys it's equipment, and does not make it.

All around, the private sector does things a lot better, and cheeper then the government.

If this is the case, why would you want to move something that's done so poorly in the private sector to the government with hopes of it getting better?

And in reality, our system is the best in the world if you remove the cost. Your going to look to Government to remove cost? 

Just to address some of your claims...

Private security forces aren't cheaper in fact private contractors get paid more than U.S. soldiers.  The reason they're contracted is because the U.S. military is stretched thin or they simply don't want to move some soldiers from non-active regions like South Korea and Japan.

How is private healthcare cheaper?  For example doctors and nurses in the United States get paid far more than their counterparts in countries with universal healthcare.  Perscription medications are more expensive in the United States.  Hospital bed stays are also more expensive in the United States as well.  There is also more overhead in their dealings with so many different health insurance companies.

Private education may be better but they have the luxury of not having to accept special needs children or follow some guidelines that public schools do.  There is more overheard with public schools some of which could be removed to help save money, for example getting rid of more non-teaching staff.

As for private roads being better and cheaper than public roads, read this: http://www.uspirg.org/uploads/Fz/KM/FzKMHurzDgFl63HW6BliVw/Private-Roads-fact-sheet-WEB-vFinal.pdf

I think some people seem to feel that everything can be done better by the private sector, but when it comes to healthcare do you really think it should be run for profit?  Think about how many hands are already in the cookie jar in the United State's healthcare system.  Think about the fact that insurance companies are constantly fighting with their customers in the denial of paying fees.  People can post horror stories about the Canadian or British healthcare systems for example but they pale in comparison to some of the ones from the United States.

*Edit: Oh and since you excluded the judiciary because it's mostly run by each State, you should look up how univeral healthcare is run in Canada since I think you may have the wrong idea about it:  http://en.wikipedia.org/wiki/Health_care_in_Canada