I can think of three models that make sense. The first would involve judicial enforcement. In other words, if the budget is not balanced under whatever specific language is adopted, someone would have standing to sue and stop money from being spent. The second would be self-enforcing. In other words, the amendment could contain a legislative trigger that would be activated if the budget was unbalanced, saying, for instance, that any additional spending would have to approved by a supermajority of Congress.
The third view would treat the amendment as aspirational. Advocates of including positive rights in the text (the right to housing, the right to education, or the right to a job) often say that the point is not to make these rights judicially enforceable. Instead, the idea is that their codification will change the political culture and exert a strong pull on elected officials. The same could be true for a balanced budget amendment.
I don't think proponents of the BBA anticipate or would be satisfied with options two or three. But with respect to the first, it is worth noting that -- unless the amendment contained specific language privileging spending cuts over all other tactics that could be used to balance a budget -- judicial enforcement could easily include injunctions to raise taxes or sell off government property.
And if they do cut spending, how exactly would they determine which programs to cut? Would it just be the ones the judge disliked the most? Finally, a way for Jack Weinstein to get us out of Iraq!