I think it's highly unlikely that a single payer system will be implemented in this country any time in the foreseeable future. Whatever the advantages or disadvantages of such a system, it would be a massive change in the way that healthcare is managed and there just isn't support for such an upheaval in the system. If you consider that this would involve basically the dismantling of all insurance companies, the displacement of hundreds of thousands of workers and potential loss of profits to many very powerful and influential organizations, you can imagine the kind of resistance that such a change would face. Even if something like this were to gain ground, it would take many years to implement and transition to a new system, so I think it's not likely that there would be substantial risk to coding employment opportunities for a long time to come.
That said, I actually think that the coding profession is a good place to be in a system that is going to be changing. My experience has been that coders are well placed to weather changes - the coding profession, and the continual growth and education that accompanies it, positions coders very well to become experts in understanding how this complex system works. Coders who maintain and develop their skills and expertise can play an important and valuable role in helping to navigate the changes that healthcare will inevitably undergo, whatever those may ultimately be.