MarketWatch tackles this question. The article mostly considers the dueling Clinton/Obama “mandate” requirement for a national health insurance plan for the nation’s uninsured:

"Many analysts believe a requirement that individuals buy health insurance -- when paired with subsidies for people who can't afford it, effective purchasing pools and easy enrollment -- is a critical mechanism for extending coverage."

National health care advocates argue that health insurance mandates should be required, the same way that automobile insurance is required for drivers. They recognize (correctly) that this is the only way to cover the high costs of the elderly and the sick (by forcing younger, healthier Americans to directly subsidize them through mandated enrollment).

I have never understood this auto insurance analogy. Sure, states require that drivers have liability insurance, that is, that drivers have insurance which cover the costs inflicted upon the counterparty in an accident. But states don’t require drivers to enroll in comprehensive coverage for their own car, which would be a much more valid comparison.

There’s no external cost to an individual’s illness. If I get sick, the cost is borne by me and me alone. We don’t purchase insurance to cover the costs of those we infect when we cough in a crowded elevator. Comprehensive auto insurance would run into the same problem as health care if it had a mandated requirement. Owners of old, beaten up cars would never enroll in comprehensive coverage by themselves. They would recognize that the perceived benefits from such insurance for them would never justify its costs. This is why it’s so much more expensive to insure a new car, because the insurance pool is overwhelmed by newer cars, which are more expensive to insure.

A mandated comprehensive insurance policy would effectively subsidize new car owners at the expense of older, used car owners. It’s like the health insurance problem in reverse. How many drivers of a 1987 Ford POS would be willing to subsidize the insurance costs of a 2008 Ford Mustang?