> (I really hate the phrase "tyranny of the majority", by the way, because it simply isn't a good way to describe democratic voting, where the majority is emergent and not determined ex ante.)
Nothing about the phrase actually requires the tyranny be remotely permanent, and nothing about the concept of tyranny requires it either. Indeed, it's actually more poignant that the tyranny is both ephemeral and, more importantly, inevitable. This is the real issue. It's easy to comprehend the issue by looking at semi-permanent states [1], like Marxist class divisions or political polarization, but those are consequences.
When you place something to a vote and fail to achieve consensus, you have a majority whose will is being enacted upon a minority. This is commonly celebrated by moronic catchphrases such as, "the right side of history," but you still have a winner and a loser. And when the ephemeral majority seems to crystallize from the aether into an unmistakable demographic of some kind, you really have to wonder about this "emergent majority" concept.
The fundamental American problem is that it is incapable of trusting its government. (I can't speak to other governments; I don't live under those.) This lack of trust is well-founded, but that doesn't make it any less crippling. I said below that the appropriate counter to the tyrannical majority is a strong executive. The executive is capable of saying, "No," to a popular opinion in a way that the legislature cannot. (Indeed, this is a role Americans have shoved onto the judiciary, which means we can't actually say no until someone files a lawsuit.) The interplay between the legislature and the executive (the vote, the veto, the super-majority overrule, the refusal to enforce, the impeachment) is exactly the solution being proposed.
None of it works without an executive willing to exercise its options. See Obama's refusal to enforce immigration laws, for instance. (For the sake of this "academic debate", let's presume that he could enforce them to the letter if he wanted to.) That is a check against tyranny of the majority. So naturally, well... see for yourself [2]. This isn't meant as an anti-Republican statement; it's just the most recent example I could bring to mind off the top of my head.
The trust part comes back when you ask, "Why doesn't a minority group tyrannized by a majority group just leave?" You know, secede. This comes back to the emergent majority you spoke of: if you trust the majority to, you know, not be dicks about it [3]. To not always be the majority, then secession isn't necessary. You can expect that the issues will change and you'll be in the majority. Of course, what's happened with the polarized political class in America is that you stick around because you figure you can win next time.
This is a problem. It is the exact opposite of what you need to make sure that a majority is an emergent majority. Instead of melting back into an indeterminate goo and forming new majority/minority groups in each vote, you have battle lines being drawn for a budding civil war. And that's as far as I've figured out.
[1] "State" as in "state of being", not as in "nation-state". My thesaurus powers have failed me.
[2] http://judiciary.house.gov/index.cfm/2015/3/at-the-flick-of-...
[3] Book recommendation: http://www.amazon.com/Talking-Strangers-Anxieties-Citizenshi...