Estuary Urgent Needs Priority Program Act - Amends the Federal Water Pollution Control Act (commonly known as the Clean Water Act) to revise the National Estuary Program by requiring the Environmental Protection Agency (EPA) to make competitive awards to address urgent and challenging issues that threaten the economic and ecological well-being of coastal areas, including extensive seagrass habitat losses, recurring harmful algae blooms, unusual marine mammal mortalities, invasive exotic species, and jellyfish proliferation limiting community access to water during peak tourism seasons.

Requires the EPA to give priority to national estuary programs that are not part of the Geographic Programs as described in the Consolidated Appropriations Act, 2014.