It leads to skyrocketing demand for healthcare (as people no longer have to pay directly out of pocket) but does nothing to increase the supply of healthcare (and often restricts the supply with regulations and taxes), which leads to shortages and rationing of care.
The only way to keep the costs under control is to bring more supply onto the market, deploy new technology and new developments in medicine. This means removing those regulations that get in the way, and investing things like research, electronic medical records, reforming tort laws and addressing rising tuition for new healthcare professionals.
Denying people care, regulating/taxing supply off the market, and/or rationing will only serve to ensure that demand is curtailed. Whether that occurs through rationing, pricing people out of the market or denying assistance to those who cannot afford it the affects are same. And it seems the extremes in both parties, while supporting entirely different approaches, both would lead to the same outcome.