Well, part of the issue is that it's only been a few hundred years since we gave the big "EFF YOU AND YOUR DAMN TEA TOO" to the UK. :o
The founding fathers that most Americans are taught to revere believed in life, liberty, and the pursuit of happiness, not happiness handed to you on a plate. There was to be no king or queen, no all powerful government. A phrase bandied about often is "a government big enough to give you everything is big enough to take everything away" .
No, we do not necessarily and whole-heartedly trust our government. I don't that's a terrible thing; Hitler was an appointed member of government FFs!
As far as socialism/communism being seen as an evil thing: I don't know about the rest of the country, but the area I grew up in was heavily settled by Finnish immigrants. Most of our older family members still tell stories about great grandfathers or uncles or whatever who, many many years ago, went to build socialism in the Soviet Union and were murdered in Stalin's Purges.
That being said, I like, support, and voted for Obama. I think the health system we've got is terrible and definitely needs an overhaul, but I'm not utterly convinced that Obamacare is absolutely bang on in all respects.
Do I have health insurance? No. Have I ever been turned away and not been treated? Never. Doctors have sent me home with free sample bottles of pills, only charged me for tests and not office visits, examined me at the same time as my son who does have insurance, etc, anything to keep my costs down. The state paid for my son's birth, including epidural, and all my prenatal appointments. What they didn't pick up, the Catholic hospital where I gave birth did.
Do I think everyone should have access to some sort of health insurance? Of course I do. Do I think that people should be forced to buy insurance? Absolutely not. To me that feels the same as governments around the world saying that their citizens cannot homeschool their own children if they choose to- a fucking outrage.