The only thing that wins popular votes is ... having a majority of voters voting for it. Doesn't sound so bad does it? At least until you start to introduce the petty tribalism of "I don't want those folks who ain't from round here telling us what we can and can't do".
The real question is: there are obviously different "ideal sized bodies" for a popular vote controlled democracy, depending on the issue at hand. It probably is right that "folks from round here" get to decide a bunch of issues, without having to convince the whole country. And there are issues where you really should only be able to move forward with a popular vote across the whole country. So the question is: what's the right scale/scope of the voting entities for different kinds of issues?
I don't know the right answer, but I'm fairly sure that the states we have right now are not the correct choice for a lot of issues.