Previous drafts of such a Balanced Budget amendment attempt to be somewhat realistic, they would allow deficit spending in time of "National Emergencies", presumably war or severe recessions.
If the feds ran a Clinton era surplus of about $100 billion/yr it would only take 180 yrs to pay off the national debt.
Unfortunately, the balanced budget amendment draft that was last voted on in congress, the one the tea party folks were advocating for during the 2011 Debt ceiling standoff, wasn't even a real balanced budget amendment. It contained a bunch of even more nonsensical provisions such as constitutionally restricting spending to a fixed percentage of GDP and requiring supermajorities in congress for any and all tax increases.