Switzerland has a feature like it, in that a supermajority is required to pass a non-balanced budget. In practice, their budgets are all balanced. See their "debt brake".
The US will never have a balanced budget with the two current political parties trading off.
It'd require, now, raising taxes beyond what even the most high-tax friendly Democrat would want, or substantially cutting Social Security, Medicare, Medicaid, and Defense spending. The Democrats will never reduce the first three enough, and Republicans will never reduce the first two and Defense enough.
Everything below those four is basically a rounding error, you could cut bits and pieces but nowhere near enough to balance the budget. And you can't cut interest payments without defaulting on the debt itself, which would create so many more problems. We need to raise our revenue by something like 50% or lower our spending by about 33%, or something in between on both.
We didn't unbalance the budget in a year. It won't take a year to fix it.
If we had proper plans to move in the right direction I wouldn't mind that at all. Instead we're blowing it up further.
Personally I'm fine with proper aggressively progressive taxes and that alone would be a huge help. But we do need to cut defense spending and yes, Social security. Because at this rate Millenials aren't getting Social Security anyway.
The US is the only democracy in the world that has this feature or anything like it.