Nurses for Under-Resourced Schools Everywhere Act or the NURSE Act - Authorizes the Secretary of Education to make competitive matching demonstration grants to local educational agencies (LEAs) in which the student-to-school nurse ratio in each of their public elementary and secondary schools is 750 or more students to every school nurse to pay a specified federal share of the cost of reducing such ratio.

Gives grant priority to high-need LEAs that demonstrate: (1) the greatest need for new or additional nursing services for their students, or (2) that they do not have a school nurse in any of their schools.

Defines a "high-need LEA" as an LEA for which not fewer than 10,000 or not less than 20% of the children served are from families with incomes below the poverty line.