All of the above. Some doctors quit, and many more would-be doctors change their minds, because it isn't worthwhile to be a doctor any more. Millions of people who would hesitate to go to the doctor with every minor ailment, if they were paying for service, flock in for medicals once it is "free".
Plus, above all, within the total health care industry budget, an ever increasing proportion goes to pay for bureaucracy rather than treatment. That, after all, is what government does well: make jobs for paper shufflers.
The outcome is that costs keep rising, but less and less is spent on medicine.