According to this ABC News story about the ongoing controversy over filibustering of judges,
The filibuster has been used historically by the minority party, which can’t win with a vote count. Democrats have opposed the filibuster before — in the 1960s, they accused Republicans of using it to block civil rights legislation.
According to the Senate Historical Office, the record for the longest individual speech is held by the late Sen. Strom Thurmond of South Carolina, who filibustered for 24 hours and 18 minutes against the Civil Rights Act of 1957. To keep the floor, he read some of his wife’s recipes and passages from novels out loud.
But Thurmond was a Democrat in 1957, and it was Democrat Robert Byrd who famously filibustered for 14 hours in a failed attempt to stop passage of the 1964 Civil Rights Act (in fact, 21 of the 27 Senators who voted aganist the 1964 Civil Rights Act).
The real, rather than imagined, sin of the Republican Party was making room for the likes of Thurmond after they left the Democrat Party.
Source:
Primer: Judicial Nominees and the Filibuster. ABC News, Annie Chiapetta, April 25, 2005.