Passage of a BBA is not just implausible; it also would be unwise. Like the doomed 18th Amendment, it would enshrine partisan policy priorities in the founding document of the republic, which was meant to structure the democratic process, not rig its outcome in advance.
It would invite a hyperactive judicial intervention in the budget-making process that would throw the separation of powers completely out of balance. Previous BBA proposals explicitly banned courts from raising taxes to balance the budget but did not otherwise limit judicial enforcement. This means the judiciary might well attempt to set specific levels for every category of spending or otherwise shape budget priorities in an effort to enforce the Constitution. Such a perversion of republican government would raise the stakes of inter-branch hostility and distrust to unprecedented levels.
And Congress would have strong incentives to evade the spirit of such a law. If you think the official scoring of budget proposals is torturously politicized now, wait until constitutionality is at stake. Be prepared for a radical reimagining of just what phrases such as “gross domestic product” and “taxes” mean. And though the amendment includes provisions for exception — waiving spending limits in the case of a declared war, for instance — they are all but certain to prove unequal to reality and subject to abuse (think wars of fiscal choice).