Let’s back up a little here for our non-U.S. friends and define some terms.
Social Security - the United States program for elderly and disabled. Soert of a government pension plan.
Medicare - a U.S. health insurance program for people receving Social Security.
Medicaid - an insurance program run by each individual state for their residents who are either too poor or ineligible for private health insurance. (Blue Cross is simply one of many private insurance companies)
Some states, counties and cities operate their own hospitals and health clinics, or subsidize private facilities in their areas. This is supposed to ensure that no one is deprived of health care.
In real life, Medicare does not provide very complete coverage (prescription drugs, for example, are not covered) and private insurance plans that supplement Medicare can range from excellent to very bad, and be very expensive.
Medicaid programs have very restrictive income limits, so a person can be working at a minimum wage job but earn to much to qualify for that state’s Medicaid program. Also, private health care givers are not required to accept either Medicare or Medicaid programs.
Private insurance plans do not have any standards to meet, so they can range wildly in price and quality of coverage. Also, private insurers are free to refuse coverage to those they feel are high-risk.
That leaves publicly owned or subsidized clinics as the provider of last resort. But health care costs are rising too quickly for most public agencies to keep up with them. Patients are expected, in theory, to contribute to the cost of their own care, but many do not pay their bills. Also, particularly in rural areas, health care providers simply may not exist, forcing patients to travel many miles for care.
Any government program that calls for universal health care coverage faces debate on three issues:
The cost to the government/taxpayers
The argument that the government will inevitably set the price of service and/or limit the amount or services a doctor can prescribe
Whether individuals and health care providers can or should be permitted to purchase private insurance in addition to the universal program – which would lead to providers who would select only patients with superior coverage/ability to pay, which would cause the same problems as the current system.
I hope this clears things up a little.