How do we know? Consider this little gem from Article V of the Constitution:
No State, without its Consent, shall be deprived of equal Suffrage in the Senate.
Note that the amendment process to which this refers already requires super-majorities: 2/3 of both houses of Congress, and 3/4 of the state legislatures.
Would it be enough for all 49 of the other states vote to deprive the 50th of equal suffrage in the Senate? No, it would not. This is what consent means. Where consent is required, there isn’t a majority big enough to substitute for it.
Why does this matter? Because the most important sentence in our Declaration of Independence — the document that explains why we needed to form a new kind of government, and what kind we were forming — is this:
That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed.
Not from majorities, or even super-majorities, or even all-but-one majorities. From consent.
If you’re looking to explain how America came to be a country so bitterly divided, here it is: We’ve forgotten, or chosen to ignore, the difference between consent and majority rule. So instead of looking for ways that everyone can stick together, we constantly have half of the people looking for ways that they can stick it to the other half.