Budget Before Borrowing Act of 2013 - Amends the Congressional Budget Act of 1974 to make it out of order in both chambers to consider any bill or joint resolution, amendment, or conference report to extend the public debt limit unless a concurrent resolution on the budget has been agreed to and is in effect for the fiscal year during which such measure is being considered.
Permits: (1) waiver or suspension of this prohibition in either chamber only by an affirmative vote of two-thirds of its Members, and (2) its successful appeal from the ruling of the Chair in the Senate only by an affirmative vote of two-thirds of its Members.