I am aware of two general arguments.
The first relies on inter-personal utility comparisons and goes like this: The marginal utility of a dollar is much higher for poor people than rich people, so in a utilitarian spirit, we can justify taking more marginal dollars away from the rich and giving them to lower income people.
(1) interpersonal utility comparisons are at best tricky and more likely impossible. We cannot rule out the case that the Sultan of Brunei gets more utility from another dollar than a slum dweller in Mumbai, and that in a utilitarian spirit, we should tax the slum dweller and give it to the Sultan!
(2) This is a case for redistribution, not for progressive taxes just to fund government generally.
(3) There is no reason for the argument to apply only inside national borders. Under the assumption of uniform diminishing marginal utility of money, we should be taxing poor Americans and giving it to the slum dwellers of Mumbai (or if we really have a utils machine, perhaps to the Sultan of Brunei).
The second argument is Rawlsian, and it goes like this: If we got together to set the rules of the game, without knowing what our socio-economic positions would be when the game was played (i.e. behind the veil of ignorance), we would all agree that rich people should be taxed at a higher rate and the money be redistributed to the poor.
Note that the same 3 notes above to argument #1 also apply equally here. We are taking uniform diminishing marginal utility of money as given, it's an argument for redistribution, not general funding, and, here even more than ever, it's a argument that should be applied globally.
Behind the veil, we don't know whether we'll be living in Norman Oklahoma, a slum in Mumbai or a palace in Brunei. The Rawlsian veil argues for higher taxes on most Americans with redistribution done on a global scale.
Now there's also the "you didn't build that" argument, but that seems more of a case that the rich should pay more taxes than the poor, which, certain extreme cases to the contrary notwithstanding, they generally do, and not a case for higher tax rates on the rich.
Are there other ways to make the case? Let me know in the comments