Democrats need to run on expanding and strengthening Medicaid, a public option to bring down costs and increase competition in the exchanges, and dropping the Medicare age to 55 or so.
Even as a single-payer supporter, this is what I've long believed. I think the two biggest failures of the ACA were the failures to adopt a public option and to start reducing the Medicare eligibility age, especially the latter. The more people we can get on to government-sponsored health insurance, the more people will see it as a virtue over a vice. I want to incorporate as many as I can into Medicare through expanding eligibility.
I think lowering the age to 55 would be a good start (maybe even go lower to 50), but I'd also like to see the program start including those otherwise uninsured under 18.
And to the OP, assuming you can understand nuance here, single-payer is not socialized medicine. It's socialized health insurance. In other words, the government pays the bills. It doesn't control the pharmaceutical industry, hospitals, or doctors or nurses. The UK has socialized medicine wherein the NHS (as I understand it) controls the entire healthcare system. I think the system in the UK is more analogous to the VA system. The single-payer (Medicare-for-All) system that many progressives argue for is based on the Canadian system and essentially an expansion of Medicare as we currently know it.