The Founding Fathers were political scientists, experimenting with a new form of government, a constitutional republic. Their prime directive was the dispersion of power. The American Revolution was a revolt against the concentrated central power of monarchy, as so eloquently expressed by Thomas Paine in Common Sense.
The Founders disliked democracy almost as much as they did monarchy. Mob rule, or tyranny by the majority, was an actual threat during and immediately after the Revolution. If you’re interested in the subject, I recommend The Founding Conservatives: How a Group of Unsung Heroes Saved the American Revolution, 2013, by David Lefer.
In addition to dispersing power, in the most basic sense, the Constitution is about protecting the minority. That concept was central to everything they did. One aspect of that protection is the provision for supermajorities. They wanted to preserve the libertarian form of government they had created from being amended out of existence by transient and excitable majorities. So a 2/3 supermajority is required to even propose an amendment. Congress needs 2/3 to propose, just as the States, under Article V, need 2/3.
It’s very hard to get a 2/3 majority in this country, and always has been. That’s the way the Framers wanted it. In today’s hyper-partisan politics, it’s virtually impossible. But the Balanced Budget has a chance, because it’s supported by 3/4 of the people, if not the politicians. The Democratic Party has become the party of government, and most people don’t want more government.
But Congress has, on occasion, assembled 2/3 majorities in both Houses to propose Amendments, and on 28 such occasions the result was an Amendment to the Constitution. There’s no reason to think State Legislative leaders would be any less adept than Congressmen at occasionally reaching a 2/3 consensus. What can the Republican and Democratic State Legislative leaders agree on? We should get some idea at the Phoenix Convention of States.