Undemocratic, yes....but it is a totally "republican" institution (meaning of or representing a republic)
I am tickled to death that our founders saw in their wisdom to set up the senate the way it is. I thought it was always the other side who went to hollering, "we're not a majority rule country!!!!" Again, I'm glad we're not. I'm glad I don't have to live according to laws made to govern Californians, New Yorkers or whatever. Got a neice and nephew who live in NY...egads, some of the stories they tell about laws governing everything from snow to trash to guns to vehicles.....yep, I'm glad those rules aren't universal just because they come from a "more populous" state.
My point is simply that a super-majority requirement for bills to pass the Senate has no constitutional basis. That's all. It's a construct of the Senate rules and nothing more.