If I didn't have health insurance and I need to see a doctor, I guess I would pay for it out of pocket if I felt it was serious enough to warrant a visit. However, I would pray that it doesn't turn out to be something really bad (cancer, long illness etc). There's also the community health clinics available locally.
I don't think simple checkups are out of range for most Americans. Most of us can afford to go see a doctor, even without health insurance. The problem is not having catastrophic insurance. Medical bills is one of the top reasons that people go bankrupt in this country, so obviously, having medical insurance is very, very useful---but even that may not be enough. Even for something like simple surgery, it can get very expensive very fast.
However, I think the people who 'fall through the holes' are those with chronic illnesses. I have a good friend who had cancer while in college. She eventually underwent surgery but afterwards, she required a lot of follow-up care and chronic medications, and an assortment of other illnesses also appeared due to her weakened state (she was always in precarious health).
For people like her, not having health insurance is scary. She's too 'healthy' to qualify for disability or any medicaid programs but she requires hundreds of dollars worth of medication a month, and constant checkups by specialists.
I remember there was a time when she couldn't find a job that gave her health insurance, but luckily her father had good insurance and he covered her by paying extra under some clause under his insurance policy at work.
But for people like my friend, health insurance is a real issue. For people like her, I don't think the current system works very well. If she was to lose her job the next day, and had to work in temp positions with no benefits, her savings would run out pretty quickly just on medications alone, and trying to get gov't insurance could take a long time (and she may not qualify...), during which she would be really pressed to cough up money for the medicine she needs.
For most of us young, healthy adults, it's not as big of an issue, but I don't think health insurance should be underestimated in its importance. Like any other type of insurance, we don't really feel it's absence until we need it. I think it's irresponsible for people not to get insurance if they can afford it, and I'm thankful I have always been covered by health insurance.