To what extent did Southern governments and states resist the Supreme Court’s ruling in Brown v. Board?

Southern states went to great lengths to avoid integrating their public schools. Richmond News Leader editor James J. Kilpatrick called for states to organize "massive resistance" to integration.
The state of Virginia, along with other states, did manage to organize massive resistance to public school integration. Senator Harry Flood Byrd of Virginia created what he called the Southern Manifesto that argued that integration violated states' rights. His manifesto was signed by 100 conservative Southern politicians. Meanwhile, Virginia began closing its schools rather than integrating them. The Virginia General Assembly supported this move by voting to end state funding to any school that integrated. The Assembly also passed a law appointing a board to decide what school a student would attend; these board decisions were based on race.
In a famous case, Prince Edward County in Virginia shut all its public schools in 1959 when the federal government tried to force it to integrate. The Prince Edward Foundation opened private schools for white students, but the county provided no schools for blacks. Schooling for black students was provided by what blacks and Quakers could scramble together.
In Louisiana, Alabama, Arkansas, and seven other Southern states, the state legislature tried to use interposition (the state's right to declare a law unconstitutional) to prevent integration. However, the U.S. Supreme Court determined this was illegal. In Little Rock, Arkansas, Eisenhower called in federal troops in 1957 to enforce school desegregation after whites refused to integrate.
Overall, whites in the South were extremely and actively resistant to the idea of school integration.
http://www.liquisearch.com/interposition/school_desegregation