No, people want to pay for things with their taxes. The are not, in fact, idiots. They don't want predatory capitalists taking a cut, and figure, correctly, that government is more trustworthy than a man with a profit motive and no morals.
People recognize that certain endeavors are just not well served by a capitalist free market. Health care is a primary one that simply doesn't work unless heavily regulated or run by the government. You do not know what is wrong with you. You do not know how to fix it. You can not shop around for a new liver.
As it is, we are basically running health care like a for profit government, and we are getting the worst of both the public and private worlds. Health insurance amounts to a system of taxation that forces the healthy to pay for the sick, and lets a third party take a huge cut. Replace health insurance with actual government taxation and what have you lost, except for the greedy bastard trying to mark up your heart medications? Nothing.