It is an odd argument for many reasons, but it seems to be the one that is given more often. Yet I've never seen any specific reasons why a single-payer system can work in e.g. Finland and Sweden and not in the US.
Healthcare benefits from having a larger population, and it is harder to provide quality care for a smaller population (read more expensive). Yet Finland spends less per capita and has better outcomes.
Imagine trying to roll out one giant healthcare system across the EU. The challenges of rolling out single-payer healthcare across the U.S. would be more similar to this than to one individual European nation, both in terms of scale (~330m vs ~450m population) and in complexity: it would require a ton of political coordination between different entities, as the individual states have a great deal of power.
Healthcare benefits from having a larger population, and it is harder to provide quality care for a smaller population (read more expensive). Yet Finland spends less per capita and has better outcomes.