My problem with libertarianism, and also why I believe is the reason why no industrialized nation on earth has adopted the ideology, is that ultimately its a utopian belief system that makes a lot of sense in some areas but is completely impractical in others. Take health care for example. You stated that you life on a very modest salary but you can still afford insurance. You also pointed out that you made payments to pay unpaid medical bills after a 4 day hospital stay. That is good and shows some personal responsibility on your part.
However, say God forbid you were diagnosed with something like stage 4 cancer. You have a poor prognosis because of recurrence rates for your type of cancer, but your oncologyst believes that your cancer is treatable in the short term. Basically, the cancer will most likely kill you, but it could take a few years to do so. So you go in for surgery to remove any operable tumors, and then you start chemo. Your insured so 80% of these costs are covered right now. The problem is that you get so sick in the short term that you either lose your job and thus your insurance associated with it, or you are not able to work enough to pay your insurance premiums. So you lose your insurance. At this point, the hospital you are getting treatment from will most likely refer you to a University Hospital. Thats not really a problem in and of itself, because if you have cancer you should have been going to one in the first place because university hospitals almost always have the best cancer centers. That university hospital would then come to you about signing you up for temporary medicaid, you would sign those forms they bring you for it because they want to be paid to treat you, and thats the only way you can possibly pay for that treatment (hundreds of thousands of dollars). So in that situation you would indeed be in "DESPERATE need of your government".
Now you are probably thinking - "wait a second, I could go to a charity hospital for treatment". Maybe so, but most likely that hospital would be hundreds of miles away or even farther and thus it would not be a viable option for you. The reason being is that you still have to live until you die. Thats the problem with dying, many times it doesn't happen very fast. So in the mean time you still have to work when you can to meet your needs of food, water, and shelter. If you are too sick to work at all, then you will be in desperate need of government again when you sign up for disability.
The tea partiers and some libertarians have some nice ideas about how the world would work without those social safety nets, but as you Yogi Berra said "in theory there is no difference between theory and practice. In practice there is. "