One of the myths is that Medicare has lower administrative costs than private insurance, and thus is the model for efficient health coverage. (This was an argument made by a woman at a forum I spoke at, before she resorted to labeling me a "tea bagger" and "birther", as though that undermined my factual analysis of health care proposals).
But this idea is a myth; a Heritage Foundation study finds that on a per person basis, Medicaid's administrative costs are higher than private insurance. While Medicare spends a lower percentage on administration, its totals costs per person far exceed those of private insurance (given it serves an older audience), and it administrative costs per-enrollee is higher. CAHI also has a recent report on the administrative costs of Medicare and Tyler Cowen weighs in on this debate with a few comments, including that "administrative costs" include the benefits of investigating fraud abuse, which Medicare - and Medicaid, as the Pennsylvania Auditor General found - does a poor job of.
Paul Krugman tries to "refute" Heritage's analysis by arguing that as a percentage of spending Medicare has lower administrative costs, which is why he doesn't have a Nobel Prize for Refuting. Heritage economist Robert Book then takes Krugman to school in a comment about the administrative costs of Medicare.
The appropriate measure is administrative cost per person, and by that standard Medicare is more expensive than private health plans. This point stands unrefuted.(HT to Greg Mankiw for some of the links)