Universal health care, through single payer or any other mechanism, is simply not a priority for the Democratic Party now. And why not?
(1) no party constituency is demanding universal health coverage
(2) no liberal or left-wing think tanks, lobbyists, unions, etc. have come up with any viable strategy to implement a federalized single payer system
(3) Democratic party members at any level of elected government are not eager to attempt to "reform" health care to their electoral demise for the third time in thirty years.
The current quality/level of coverage/access to insurance through Obamacare exchanges and the Medicaid expansion suits the Democrats just fine for now.
I hate to sound like a Republican, but the exchanges part of Obamacare
is fundamentally flawed and will eventually collapse on its own weight if radical changes aren't made to it. One such radical change is single-payer, and chances are it would solve the problem more definitively than any other proposal.
(Note that I don't even like single-payer that much. The French system has serious issues for example. An NHS-type model would be infinitely preferable, but that is probably out of reach for the US in the foreseeable future.)