If I had my way Government would get completely out of health care but I do not see that as politically viable so I propose that the states rather than the Federal Government experiment with a program to provide insurance.
If any Government body should be experimenting with providing health care it should be the states rather than the federal government. The sates control medical licensing and that means that they control costs to a large extent. States do things like refusing to accept medical licenses from other states and countries that drive up costs. States refuse to accept medical insurance plans that are accepted in other sates this also drives up costs. If the Federal Government provides the money for heath care the states are not encouraged rightly license to maximize the cost benefit trade offs .
The big obstacle to the states providing health care is the danger that a state would attract the sick and poor from other states. A plan to avoid attracting sick people from out of state to the state would be needed.
The plan could include some period of time to establish residency. For example a state could have a 2 year period to establish residency before one is eligible for existing conditions. Insurance companies already police this sort of thing so it is possible.
To make the plans cheaper and less desirable to out of state people the insurance could be kept simple and minimal. Much medical care in the USA yeailds very low or even no benefit, a state plan could opt out of paying for such procedures. Since people trust Government more that insuarcne companies they could get away with refusing more care. An example or care that might be eliminated is heart bypass, there is no evidence that heart bypass surgery produces better benefits than less invasive and much cheaper care, except if the blockage is in the upper left ventricle (and even then the evidence is weak). Heart bypass is rarely done outside of the USA In the USA though heart bypass is commonly done for all kinds of blockages. The state policy would allow those who wanted to pay for such procedures to do so out of pocket but it would not pay for such procedures.
The states could also establish high means tested deductibles. Here is an article that proposes a $50,000 annual deducible. Here is me advocating a deductible based on income.
States could initiate some other experiments to save money. Here is Dean Baker's proposal to reign in costs.