Drinking Water Supply Assistance Act of 2013 - Amends the Safe Drinking Water Act to exempt any pipe, pipe or plumbing fitting or fixture, solder, or flux that contains brass from certain prohibitions against the use of lead pipes, solder, and flux under the following conditions:

• a supplier of water owns the brass before enactment of this Act;
• the brass is used to prevent or mitigate a municipal budget deficit or an interruption in service of a public water system; and
• the supplier of water is otherwise in compliance with all laws and regulations, except monitoring requirements regarding lead in water.

Makes the exemption inapplicable to a municipality if the Administrator of the Environmental Protection Agency (EPA) determines it would result in an unreasonable risk to public health.

Directs the Administrator to: (1) consult with and seek the advice of the National Drinking Water Advisory Council on potential changes to federal regulations pertaining to lead; and (2) request the Council to consider sources of lead throughout drinking water distribution systems, including through components used to reroute drinking water during distribution system repairs.