It depends. They already do work together, the model just needs to evolve. How? By respecting the boundary between government and the private market and the application of private sector management principles, the government can work with the private sector to insure the uninsured and lower cost.
In 2006, Massachusetts enacted health care reform similar to the Affordable Care Act. Today, Massachusetts insures almost 98% of its residents, leading the nation on that measure. On the other hand, it also leads the nation in health care costs 36% higher per capita than any state in the country.