When you're leaving your job to start a business, the assumption is that you have some money saved. You're guaranteed not to be turning profit for a certain period of time. Depending on how lucky and how good you/your idea are, that could be anywhere from a month to a year or two.
Not having government health insurance just means you'll have to get your own. I am speaking here from experience: I quit my job, posted about it on HN, bought myself health insurance, and started my own software company.
How much did the health insurance cost me? 200 dollars a month. (Edit: yes, this is in the USA. IL to be exact.)
Yes, 200 dollars is not nothing. Yes, it would be nice to not have to pay that. But then again, I'm paying 1200 for my apartment, 80 for my cellphone, 80 for electricity, and I'm sure I can come up with some other monthly obligations that I have. Health insurance is maybe ~10% of my "maintenance costs" that I can't avoid.
Why aren't we arguing that the government should provide apartments for everyone so they don't have to worry about finding a place to live when they take the risk of leaving their jobs? Or require special restaurants that are publicly funded so that you don't have to worry about that, either?
I know a lot of people will take issue with this, but, keep in mind, I am not saying I'm against government health insurance. I'm saying that this isn't a very good reason for it. Going off on your own is and always will be a risky situation, unless you're already independently wealthy. By definition, it involves giving up a cushy job and steady pay for the chance of striking it rich on your own or (as in my case) doing what you love. That's the nature of the beast, and that's why we have both entrepreneurs and employees.