I would assume that Communists support a National Health Service with a fallback position that Universal Single Payer is acceptable as a compromise or interim solution until their utopia comes into being. I am not a communist, but I support Universal Single Payer for very capitalist reasons which I have worn myself out explaining to people who claim to be capitalists, who insist that USP is an NHS or that USP is some huge departure from our current mishmosh. So there is a case where Democrats are more likely (at least perceptually) to support a major issue common to people across a political spectrum, including Communists.
Now that I think about it though, given the history of how USP started in Canada as a regional system in Saskatchewan, and the fact that Canada's western provinces tend to be very conservative, maybe the "support Dems for USP" is misguided. I myself have predicted that USP will come into being, and the Republicans will take the credit for it coming to be. The Republicans are practical people, it's the aspect of them that I appreciate. They KNOW that USP is an eventuality, they simply want to skim as much money as possible out of the current system before "discovering" the savings and benefits of USP and putting that feather in their cap.
The CPUSA/wee wee/Nova dream ticket