Amending the United States Constitution
In Article V of the U.S. Constitution, there are two methods by which an amendment can be proposed for ratification by three-quarters of the states (38/50):
The United States Congress can propose an amendment via a two-thirds vote of the U.S. House and the U.S. Senate.
The states can propose an amendment at a convention once two-thirds of the state legislatures (34/50) have passed the resolutions necessary to convene it.
The Great Conundrum
While Congress has long failed to propose a Balanced Budget Amendment (BBA), the state-driven convention process is complicated, untested and difficult to unleash.
Fortunately, there is a third option.
The states can use the threat of a convention (at 33 states) to force Congress to propose a BBA, just as they did when they forced Congress to propose the 17th Amendment. The motivating fear for members of Congress is that a state-drafted BBA is likely to be quite draconian, and thus Congress is highly likely to propose a BBA of its own at 33 states.
Thankfully, we already have 27 of the 34 state resolutions required to call a convention to propose a Balanced Budget Amendment. That means we only need 6 more states to reach the 33 necessary to threaten a convention.