In this case there may be enough valid petitions to force Congress to set the time and place for an Amendments Convention to address a balanced budget amendment, period. No other subject matter may be addressed, lest the Convention exceed its authority. Before anyone starts that canard about the original Constitutional Convention of 1787 exceeding its authority, I would suggest they read Madison's answer to that charge in Federalist #40.
IOW, because Congress does not face the hurdle of Petition Aggregation, it would potentially easier for them to propose an Amendment for ratification that eliminated 2A.