It would be possible to create a system where everyone has access to medical care through a system of public loans.
The basic idea is that if a person showed up at a medical facility with a health problem, they would get a loan financed by the government. On taking the loan, the person is immediately slapped into a medical savings and loan structure for repayment.
The cost to the taxpayer is the interest on the money, plus the default rate on the loan. This is substantially lower than the cost that incurs when the public finances the care in full. The benefit is that it forces people who've failed to account for their medical needs into a structure that will force them to start account for their needs.
NOTE, the federal government is not the only stakeholder in delivering needed care. The hospital, state and local governments are generally concerned with seeing that basic care is available to all. If a hospital makes a loan, you would probably want the hospital to own the first 50% of the loan, the state to own 25% an the federal government 25%.