The Democrats could have done this of their own volition in Obama's first term, during periods where the Senate had a filibuster-proof majority. Instead, they came up with the ACA.
> Lieberman, 67, used his deciding vote in Congress to help strip out a provision for government-run medical insurance, intended to set up competition to the abuses of private companies, by threatening to filibuster the legislation.
> Senate leaders agreed to drop the public option for all in favour of allowing people over 55 to buy into an existing government-run scheme for the elderly. In September, Lieberman supported the measure, as he had when he was Al Gore's running mate. But just as it seemed that a deal was done, Lieberman scuppered it by announcing that he had changed his mind and would block any bill that expanded government insurance coverage. Obama gave way.
https://www.theguardian.com/world/2009/dec/16/joe-lieberman-...
How much more than the ACA (a campaign promise) and stimulus did you expect them to get done in the 4 months of the first term that they had a filibuster-proof majority?
https://www.beaconjournal.com/story/news/2012/09/09/when-oba...
The only way it would get struck down is if there were activist judges and if there was no political will to repair the Supreme Court. I would assume that in a world where the US political system manages to fix itself enough to pass universal healthcare that would be dealt with or fixable, because those are more urgent issues.