The great advantage of universal, government-provided health insurance is lower costs. Canada's government-run insurance system has much less bureaucracy and much lower administrative costs than our largely private system. Medicare has much lower administrative costs than private insurance. The reason is that single-payer systems don't devote large resources to screening out high-risk clients or charging them higher fees. The savings from a single-payer system would probably exceed $200 billion a year, far more than the cost of covering all of those now uninsured.
This is the argument that gets lost in the discussion too often. Because private health insurance spends so much money and resources finding ways to avoid coverage, a single payer system would be cheaper. Last month Krugman listed several western European Countries and Canada that have universal health care and spend less on it than the United States government does to cover a few people right now. That's because we're guaranteeing government coverage to a few people within a broader private system that forces health care costs up. Therefore the costs of delivering health care is high, and the Government is forced to pay the same rate to the providers as the private insurers.