Final answer:
President Dwight D. Eisenhower did have the constitutional right to send federal troops to Little Rock, Arkansas to enforce desegregation, following the Supreme Court's decision that mandated the integration of public schools and to uphold federal law in the face of state resistance.
Step-by-step explanation:
President Dwight D. Eisenhower had a constitutional right to send federal troops to Little Rock, Arkansas, to enforce desegregation in public schools. This action was justified under the Executive's obligation to uphold federal laws and court orders, specifically following the Supreme Court's decision to outlaw racial segregation in public schools.
The situation escalated when Arkansas Governor Orval Faubus used the state National Guard to prevent the Little Rock Nine, nine African American students with exceptional academic records, from entering Central High School despite a court order mandating integration.
Eisenhower's response included federalizing the Arkansas National Guard and deploying the 101st Airborne Division to ensure the students could safely attend school. This response was necessitated by the inadequacy of state authorities to abide by the federal court's decision and maintain law and order.
Eisenhower's actions fell under the ambit of the Presidency's responsibilities to enforce rulings of the federal courts, ensuring compliance with the Constitution and federal law, despite the presence of widespread local resistance and the initial inaction from state executives.
Through these measures, President Eisenhower affirmed that the federal government would not tolerate open defiance by state governments in matters of federal law, demonstrating the Executive Branch's role in the enforcement of civil rights and court-ordered integration during the Civil Rights Movement.