This, from the 2008 version of “Budget Process in the States” (National Association of State Budget Officers) answers some of my questions:
Virtually all states have some form of balanced budget requirement. These requirements are often statutory or constitutional in nature and range from requirements that the governor submit a balanced budget to requirements that a governor must sign a balanced budget. […] [G]overnors in 44 states must submit a balanced budget, and in 41 states legislatures must pass balanced budgets. […]
State debt is issued in order to finance capital projects that will serve to benefit taxpayers over a series of years. […] In the case of debt service, many of the limits are tied to general fund revenues. The limits for authorized debt may include dollar values and also be tied to authority from the legislature or from voters. States may also have policies through debt management committees that deal with a range of debt instruments beyond general obligation authority.
The document includes a table (among many others) that lists debt limits by state. Clearly a “balanced budget” does not mean “no debt.” So what does “balanced budget” mean? The National Conference of State Legislatures kind of answers that question:
What is meant by a balanced budget is not as clear as it may seem intuitively. Even the number of states whose laws require a balanced budget can be disputed, depending on the way the requirements are defined. […] Two points can be made with certainty, however: Most states have formal balanced budget requirements with some degree of stringency, and state political cultures reinforce the requirements.
Not very satisfying. PolitiFact Texas weighs in with, “[D]espite the letters of those statutory and constitutional [balanced budget] strictures, they aren’t universally viewed as mandatory.” Hmm …
