In fact it is a partial solution with difficulties. The underlying reason that the government promotes this solution is that it should lower the average cost of health care for the several who are not insured presently. This may be true. However, it does not provide incentives for more efficient health care delivery systems or for participants to make better decisions. It also means that insurers will be providing more expensive care to more people. (Not all bad, but true.) In theory, it will lead to a majority of people in the U.S. paying much higher insurance premiums, while only slowing the increase of health provider costs. (This is not denying the fact that the new coverage will be a great blessing to the roughly 30 million that it will cover 10 years from now, according to government estimates.)
Shouldn't we also be concerned with lowering the average cost of heath care for most Americans? What about actually improving our overall health? These can primarily be done by encouraging healthier decisions in the population and focusing on preventative measures. Offering less insurance coverage for diseases resulting primary from poor personal choices is one method that has been proposed to help in all of the above areas. (An example argument is that the treatment for someone who has drunk heavily all their life who develops cirrhosis of the liver should not be covered by any health insurance. Otherwise, everyone else paying premiums to that insurance company pays for this person's treatment. The aforementioned Medi-Share takes this option to keep their costs low.)
The other thing that hospitals and doctors offices need to take up is the responsibility to streamline record-keeping. Google Health agrees. It is designed for you to collect and organize your health information in one place and make it available to physicians at will. It is not very popular yet, but systems like this may become more utilized.
Finally, heath care providers need to accept that the best way to attract a greater quantity of increasingly responsible patients is to make their prices and services clear from the beginning. I should be able to easily find the relative cost for labor and delivery, certain x-rays, scans, etc. by checking with local hospitals. This will only happen if consumers (that's you!) make it known that the reason they are choosing their health care provider is because of their clear pricing. Until it's important to you, it won't be important to them.