To get such a law passed would require:
Majorities in favour of the law in both the House of Representatives and the Senate. And since there are filibuster and cloture rules in the Senate, a super-majority of 60 may be required in the Senate. As only 1/3 of the Senate is elected at any one time, the chances of there being 60 senators in favour of such an act seems very remote.
A Supreme Court that finds the act constitutional. Unlike other systems, in which it is assumed that the government can pass any law it chooses, in the USA the powers of the Federal government are delimited. It is not unusual for the court to say that a law is unconstitutional and void. There is currently a 5-4 Republican majority in the Court, and the president can't easily change it.
A population that finds this model of healthcare so good (despite higher taxation, or less money spent elsewhere) that a future president can't repeal or replace the act.
The US system was designed to work on consensus, with the House representing the will of the People, the Senate representing the various states, and the President, above politics, carrying out the instructions of those bodies. This makes it difficult for a political president to act, especially when there is no consensus.
In the case of healthcare, this has become one of the major policy differences between the parties. Unlike in (say) the UK, where all parties of both the right and left generally agree that the state has a major role to play in providing healthcare, in the US this is very strongly opposed by one of the major parties. When an issue becomes a polarising issue, it is very hard to find the consensus that the US system requires.
Healthcare is exceedingly expensive, especially in the USA. Private insurers charge more than state insurers. People with private insurance can get healthcare that would not be available on a state-managed and rationed healthcare system. There are therefore powerful vested interests in maintaining the status quo.