The bigger question should be "why is health care tied to employment?"
If IBM can create a pool of, say 50,000 people (employees), and negotiate a rate with Aetna or Blue Cross, why can't a community do the same thing?
Why can't the Govt create similar (larger? smaller?) sized pools (by zip code? Congressional districts? School districts?) and have the insurance companies bid on a rate to insure every individual and/or family in the pool just like they do if General Electric or Boeing or RJR-Nabisco or any large corporation looks for an employee health insurance plan?
It seems pretty simple to me - the insurance companies can still make their profits as they do now, they can charge a rate that they feel is competitive enough to get the business, and the "pool" of "to-be-insured" people can choose the best rate/coverage they can negotiate, and everyone in the "group" will be offered the same rate, without the fear or burden that an economic slowdown/recession/depression may not only cost them their job, but indeed, their life.
Actually, large employers often "self-insure" basically using the insurance company as a claims processor with a set of rules tuned (include this, don't include that, etc) by the employer to manage costs. Over large numbers of employees it all comes out in the wash and is cheaper than paying an insurance company to remove your risks. And there is supposed to be a wall between the insurance company and the employer/funder to ensure that they don't know who exactly is costing them money.
Unfortunately, even if you throw all the folks who don't have insurance today into a pool, their cost is likely to be (on average) higher than most of the existing pools. Basically, you have a larger percentage of uninsurables out there today than in most companies. By and large, employed people also tend to have healthier lifestyles than those who are not employed (think of the large number of folks on the fringes).
I think the bigger problem is a lack of a secondary insurance for medical. In many lines of insurance (I'll use shipping for an example), an insurance company may insure X shipping lines boats for $Y per year. X's ships have been sailing off the coast of Somalia because of their trading partners and are now more likely to be hijacked. These insurers typically have secondary insurance limiting their exposure because a small number of incidents can blow their operations out of proportion, because in most years there aren't too many piracy claims, but when they do arise it is expensive.
I think if there is a place for the government to help people get back into the private insurance market, it might be to provide some sort of secondary insurance limiting the exposure of the insurance companies in their first years of dealing with previously uninsured (but not necessarily uninsurable) clients. This would probably be a temporary institution until all players are back in the private insurance market given a rule that you cannot be denied a change of insurance (or excluded for pre-existing conditions) if you are currently insured (at least 5 years).
And I agree that access to insurance shouldn't be controlled by employers. Granted they provide an efficient mechanism for enrollment and fee payment which should continue. Leaving many individuals to pay premiums out of their take home pay would lead to fewer insured, as many make poor decisions taking risks and then trying to lay the penalties off on the taxpayer, so payroll premium payment (like tax withholding) is a good thing.
Perhaps the unemployment insurance system should be structured to continue paying medical premiums in addition to a slightly reduced benefit, as often newly unemployed individuals often make the poor choice of dropping medical insurance because they haven't saved enough for the rainy day of unemployment. Yes, it would cost more and perhaphs even discourage employment, but in the game of robbing Peter to pay Paul, preserving health is probably more important than preserving gainful employment, as most individuals will adjust quickly when their stomach is empty, but not when their stomach has a tumor.
Basically, solving healthcare is about getting people to engage in the correct behaviors - keeping insurance, making sound decisions about when to go to the doc, etc. Healthcare is provided, just not in a way that is efficient (poor use of facilities) nor encourages socially responsible use of and payment to the system.
Not everyone can afford Cadillac healthcare with no waiting and the latest new drugs and technologies as the first line of treatment. To those who can afford it, please buy the appropriate insurance and use it. For those less fortunate, I think even if the rest of us have to subsidize it to some extent, we are better off having them in a system that rewards good behavior and punishes poor choices (go to the emergency room for a cold and get sent home after waiting 6 hours to get to the front of the triage line).