Jon Cohn preaches the gospel:
Lack of health insurance leads to worse health. The precise impact isn't clear--largely because it's difficult to separate causality and correlation. But most experts I know would agree it has some impact, likely a substantial one, by making access to medical care more difficult. Still, the health effects of uninsurance--and underinsurance--are secondary to the financial ones. In other words, universal health insurance is primarily an economic security issue. Individually, Americans face severe financial hardship if they end up with medical bills they can't pay. Collectively, we all bear the price of a system that distorts our labor markets and, more generally, costs more than it should given what we get from it. So if you're doing a cost-benefit analysis of universal health coverage, a big benefit--indeed, I would argue, the biggest benefit--is vastly improving economic security for low- and middle-income (and even a few upper-income) Americans.
Economic insecurity, as Jon notes, exist both on the micro and macro levels. On the micro level, a health crisis can leave you bankrupt if you lack insurance, have too little insurance, have too high a deductible, or your insurance decides not to cover the costs of your treatment. On the macro level, the spiraling cost of health care is a massive threat to our economy. Looking into the future, if we don't restrain the growth in health spending, effective GDP-per-person (i.e, what's left after health costs) will actually begin to go down (here's a graph!), and we'll all become poorer. And my hunch is that the only way to restrain health costs in a humane and politically palatable way will be through integrating the system, bargaining down prices, and rearranging consumer incentives so soft rationing -- i.e, ineffective drugs receive less reimbursement, and so aren't as often used -- becomes possible. The Right's strategy, vastly increase people's personal financial exposure so they can buy less health care or suffer worse consequences, both won't fly politically, and shouldn't fly morally.