You are not really that naive to think that we don't all pay for the uninsured already are you?
I think the big disconnect here is some of you are talking about health care while I'm talking about insurance. They aren't one in the same. Insurance is a risk management tool. A national health care system is a society's decision that they want people to be able to go to the doctor. I'm not going to comment on whether that is good or bad. That is political and that is not the point of this thread.
My point is that if we are expecting an insurance company to suddenly "insure" a large class of people who are very high or guaranteed risks, then rates will tend to increase. To take the wildest example in an attempt to be clear: A health insurance company being forced to write a new policy for a person who is terminally ill with cancer, and to pay for treatment of that pre-existent condition, is the same thing as an auto insurance company being forced to write a new policy for, and to pay for the repair of, a vehicle which has already been damaged in an accident.
That situation folks, is not insuring risk, but financing certainty.
A few other high level points while we're on the topic:
1. An insurance company's profit is typically derived from investment income that they earn on premiums invested before a loss. These investments fuel our economy and help businesses and it is a good thing that they should continue, but if an insurer must set aside adequate reserves to pay for a higher presumed future loss, investment decreases.
2. States tend to regulate insurance, and insurance rates. Many states require an insurer to submit their proposed rates for approval before they can start using it. Others allow them to make adjustments within certain boundaries to account for market changes (for example you might be able to raise or lower them by 10%). There are also other arrangements. So not to get political but if you're having an issue with how much it's costing you, why not call your local insurance commissioner? Your own state might be the one setting the amount.
Don't get me wrong there are a ton of problems with insurance... But this thread is evidence there are a ton of misconceptions too.