Except we're not starting from a blank slate. So short of heavy-handed, dictatorial decisions how would you propose to get to a single-payer plan that covers everyone? You'll have to work with the existing hospital infrastructure, insurance companies, and citizens who don't want a single-payer system. They all get a say, too. People who act like its a straightforward solution don't really understand the problem. But to avoid sounding overly cynical, I'll throw out a couple of recommendations.
1) Expand the VA system to cover all vets, regardless of whether it's a service-connected health issue or not, without insurance. This is politically possibly the easiest step because its hard for a politician to stand up and say they aren't an advocate for better care for the troops. However, the VA is entwined with medical schools and you'd have ensure you expand the funding proportionately to avoid pissing off that constituency.
2) Gradually ratchet down the age for medicare, over decades.
(I'd also argue you'd have to get money out of politics first for any really change to have a chance)