People claim we can’t do this sort of thing here, but their arguments are fairly unpersuasive. There is good reason to think we won’t do it here for political reasons and for reasons having to do with the fact that whites in the US generally don’t want to improve the well-being of Blacks and Latinos, and this turns them off from high taxes and welfare. But if you put that political question aside, the policy side of things is not that complicated.
The US is bigger than Denmark by a lot, but with its larger size also comes a larger national income. On a per-capita basis, the US actually has quite a bit more national income than Denmark (in 2005 $PPP). So we don’t lack for the income necessary to fund a Denmark-like system.
American exceptionalism is taking quite a beating lately. As Matt discusses, things don’t have to be this way. It comes down to a question of whether we want to aim for broadly-shared prosperity, or are we happy to suffer to keep the “other” from advancing?