You are correct, most Americans do not favor a single payer system. I think it goes back to our founding as a nation, and the distrust of authority that was written into our founding documents.
Most Americans still view anything given to them by the Government as suspect, and the first words are "why am I getting this" and "if my taxes are going to rise just keep it".
There is also a pride issue at play here as well, many would see a single payer system as charity, and charity is deeply looked down upon in the US.
My generation, I'm 58 was taught if you don't have enough money, then you need to get a second job, and not to look to the Government for help, if you still don't have enough money, then family should help you.
These views are deeply ingrained in our culture, but cracks are starting to appear with the younger generation, and things may change at some point...maybe. However, when these young people start to hit age 30 or, so, their views start to change a bit and the thought of giving their hard earned $ to people who feel they are entitled to what they work for becomes less palatable, and research, depending on who is doing it, bears this out.
Speaking for myself, I think a single payer system would be a disaster in the US, I lived in Greece from 2001-2003, their single payer system is pretty bad, and last I read it was ranked just above Canada's system (so I will avoid getting sick in Canada at all costs)
Less choice, longer wait times, and worse outcomes would be the result in the US. Even those who get care at free clinics would hate it. Making changes to the affordable Care Act would be our best bet.