Recognizing the National Benefits of Flood Protection Act of 2013 - Requires a feasibility study for a flood, hurricane, or storm damage reduction project to include calculations of the anticipated: (1) reduction in damage to public and private property and infrastructure; (2) direct and indirect economic benefits, including from potential reductions in national and regional economic volatility, disruptions, and losses; and (3) benefits to public safety, including protection of evacuation routes.

Authorizes the non-federal interest for such a project to submit to the Chief of Engineers a request for a project review if the Chief: (1) determines that the project is not feasible, (2) issues an unfavorable report for the project, or (3) identifies the feasibility study for the project as inactive.

Directs the Chief to establish a panel to conduct such reviews for each Corps of Engineers division not later than 60 days after the first request for a review of a project within that division is submitted. Requires such panel to conduct a review of: (1) the feasibility study for the project; (2) the adequacy and accessibility of the economic, engineering, and environmental methods, models, and analyses used in preparing such study; (3) public comments on the project; and (4) any additional information submitted by the non-federal interest as part of the review request.

Requires: (1) the panel to submit a final report containing an economic, engineering, and environmental analysis of the feasibility study and a determination of the project's feasibility; and (2) the Chief, if the panel determines that a project is feasible, to issue a favorable report for the project.

Directs the Chief to: (1) give priority to the completion of feasibility studies for projects in areas that have experienced flooding or hurricane damage during the preceding 10 years, and (2) submit an analysis of the connection between such Corps projects and navigation and the protection of energy infrastructure.