The State of Tennessee has started something:
The State Senate of Tennessee has laid the legislative groundwork for something that hasn't been done in the United States of America since the Constitutional Convention of 1787 in Philadelphia. With a vote of 27-3, the Tennessee Senate has voted to call a "convention of the states" in order to draft and pass an amendment to the Constitution that would require balanced budgets to be passed every year.
For those who are little fuzzy on their high school U.S. history knowledge, the Tennessean explains that the U.S. Constitution can be amended in two ways. The first would require a two-thirds majority vote in both chambers of Congress, an unlikely outcome in today's hyper-partisan political arena. The second, on the other hand, requires that two-thirds of the states (34 in total) pass a resolution calling for a Constitutional Convention.
[...]But, as the Tennessean notes, the problem with amending the Constitution through a convention is that once the convention is convened anything can happen. For example, the last time the states gathered for a convention in 1787 they ended up tossing out the Articles of Confederation and forming an entirely new government based on the current Constitution.