Do you really want them voting though? I'm serious. You should care about them learning about the options more than whether or not they vote. An uniformed vote is far worse than a vote not cast.
We should be encouraging people to vote smarter, which also means not voting if you were too busy or apathetic to cast an informed vote.
And I take Jefferson's quote from your post and modify it. If he were alive today he'd probably say, "It does me no injury for my neighbor to have insurance or no insurance. It neither picks my pocket nor breaks my leg." He'd also probably re-publish his Kentucky Resolutions declaring that, per the 10th amendment, the power to mandate purchase of a private product is reserved to the People and their Legislatures..... not the Congress.
Until your neighbor can't afford to give their kid a vaccine, and your kid gets a disease and dies because he was one of those that the vaccine doesn't work on. The health of the population is in the best interest of the entire population. I don't think the healthcare law is the best solution but to say that the health of your neighbor doesn't affect you is to live in a very small bubble.
"The fundamental principle of science, the definition almost, is this: the sole test of the validity of any idea is experiment." -- Richard P. Feynman