Zero-based Budgeting Ensures Responsible Oversight (ZERO) Act of 2013 - Requires the President to submit with materials related to each federal budget transmitted to Congress by January 1, 2015, a budget for each agency that contains:

• a description of each activity for which an agency receives an appropriation in the current fiscal year or for which the agency requests an appropriation for the budget year;
• the legal basis for each activity;
• for each activity, three alternative funding levels for the budget year (at least two of which shall be below the funding level for the current fiscal year), a summary of the priorities that would be accomplished within each level, and the additional increments of value that would be added by the higher funding levels; and
• for each activity one or more measures of its cost efficiency and effectiveness.

Requires the  Director of the Office of Management and Budget (OMB) to publish guidelines to carry out this Act that shall require: (1) the baseline budget of each agency to be assumed to be zero, and (2) each proposed expenditure to be justified as if it were a new expenditure.