I don't think you're really putting yourself in their shoes.
For most people, things are were better for them before required, high-cost health plans. Most people don't get seriously sick in a given year; that's why health insurance works at all.
And for those with required health insurance, it doesn't really help.
Take me as an example: I'm 29 in NY and the healthcare plans I have available to me basically fall into a spectrum ranging from $170ish/mo with a $6000ish deductible to $600ish/mo with no deductible. At the low end of that range, health insurance does nothing to prevent a person making $15K/year from going bankrupt; $6K in medical costs is more than enough to bankrupt such a person and you don't get extra credit for going bankrupt by $6K instead of $50K. And at the other end of the spectrum, $600/mo is enough to drive many people bankrupt in itself. The plans in the middle don't strike a good balance; they just cost enough that a poor person can't build up savings so they'll go bankrupt if something does happen to them.
I'm lucky enough to have a job that pays much more than $15K, and I can actually afford my health insurance with relative ease. But for most, it's better to just take the risk and not pay for health insurance, because it's not going to prevent you from going bankrupt anyway. Except, now you can't.
And yeah, they can vote for Obamacare, but keep in mind that when you're living paycheck-to-paycheck, it's very hard to look at anything other than proximate causes of your problems. You see the tax coming out of your paycheck, you don't see the pointless military equipment it's spent on or the "privatize profits, socialize losses" companies that your taxes could regulate. And all the help the government promises you comes to nothing most of the time. You don't read the newspaper and spend mental energy on that because you're watching junk television to recover from your day, or just plain going directly to bed. You also don't have a ton of education (which doesn't mean you aren't intelligent). So you vote for the guy who promises to take less of your money in taxes and do less that you don't see.
All of this isn't finding ways to rationalize acting against their own self-interest (although that does happen too). It's a rational understanding of what's in your self-interest given the information you have, the time you have to research, and the experience you're allowed.
And when using democracy to improve your life doesn't work for decades, can you blame them for giving up on using democracy to improve their lives?