A better way to describe the program would be to call it "universal heath insurance." The idea is that by compelling everyone in the nation to participate in the insurance market, you'd cut down on what's known as the "free rider" syndrome. As the term suggests, this would be people getting a "free ride" from the healthcare system by deciding not to get their own health insurance because they've been assured that in the case of an emergency or personal health catastrophe, inexpensive care will be guaranteed to them by the government. The theory is that mandated participation would help to drive down insurance costs.
But any mandate requires an enforcement component. My fear is that a government branch with the kind of power to actually identify and penalize those seeking to avoid the insurance mandates of universal healthcare would be vast and all-powerful. The new healthcare arm of the government would likely have the same kind of power (and loathsome reputation) as the IRS.