I generally use this argument with people who really aren't Socialist/Liberal but more like moderates and the only reason why they think they should support a Single payer healthcare system is because it will be cheaper that way. And it never fails.

There is one of the following reasons why medical insurance costs are so high in America:
1) The medical insurance companies are just charging super high costs to make more profits(because they are evil and greedy). If this is the case then the Government should just create another health insurance agency which will not be evil and greedy, and not be a part of any price gouging cartel. And this govt medical insurance agency will be charging really less fees(only to make minimum profits possible) so everyone in America will rush towards this insurance agency thereby driving down the insurance costs for every medical insurance company.

2) The private medical insurance companies are just inefficient and cannot do the job they way Federal government would do. If this is the case then again the govt should launch their competing health insurance agency which will do the job more efficiently, there by charging less and everyone in America will run towards this agency and other private health insurance agencies will either be kicked out, or be forced to be more efficient.

3) The massive amount of regulations on Insurance sector, makes it impossible for health insurance agencies to charge less fees and follow them at the same time. If this is the case (which probably it is) then there is no way a Nationalized Health care system be more cost effective than private health insurance care. That simply means that a Nationalized healthcare system will transfer the extra costs to the taxpayer, in which case this system is equally bad(if not worse) than the current system. The government will either NOT follow the regulations(in which case why not eliminate the regulations now and reduce the costs), or the government will follow the regulations(and since the govt is no more efficient than private sector, it will be cost the same). Either way the private health care sector for middle class will be killed because the taxpayers will be paying for healthcare anyways.

Some people still do not agree after this argument, but they can now, never say that govt will do a better job than private sector, they all say 'well it doesn't matter, all I am saying is that I cannot afford the private health insurance and I want the government to pay for it(i.e. I want other taxpayers to pay for my insurance).