There already is a single payer system in the US that only serves a small segment of the population. It's called the VA. While the VA does a lot of good for a lot of people and some people actually get GREAT care through it, it is also severely mismanaged, extremely bureaucratic, and many people have died while waiting in a line to get in the line to be treated. In other words the US Government has proven that it cannot properly manage health care in this smaller segment, I KNOW they could not do it on a larger scale.
The term "Single Payer" does NOT mean patients get one bill, it means the US Government essentially becomes the insurance company for everyone and all insurance companies go out of business. Right off the bat that would put a few million people out of work, so not off to a good start. Just like insurance companies can choose what drugs are covered, the USG would too, but now that choice could be influenced by lobbyists and political donations. With the USG paying all the bills you can bet that to save money they would regulate people's choice to do anything that could cost them money.