Orval Faubus, Arkansas governor, famously resisted Brown v. Board by deploying the National Guard to block the Little Rock Nine in 1957. His stance aligned with massive resistance to desegregation.
The speaker most likely to support Faubus would argue:
"The federal government should not interfere in the affairs of the states. The states should be allowed to decide for themselves how to deal with the issue of race relations."
Federal courts and ultimately Eisenhower's deployment of the 101st Airborne enforced desegregation, rejecting the states' rights doctrine in this context.