You must have missed where Robert Byrd filibustered the [Civil Rights] bill for 14 hours, unsuccessfully. For 57 days Democrats filibustered, and eventually failed.
U.S. Senate: Art & History Home > Senate Stories > 1964-Present > Civil Rights Filibuster Ended
In the early 1940s, a politically ambitious butcher from West Virginia named Bob Byrd recruited 150 of his friends and associates to form a chapter of the Ku Klux Klan. After Byrd had collected the $10 joining fee and $3 charge for a robe and hood from every applicant, the "Grand Dragon" for the mid-Atlantic states came down to tiny Crab Orchard, W.Va., to officially organize the chapter.
As Byrd recalls now, the Klan official, Joel L. Baskin of Arlington, Va., was so impressed with the young Byrd's organizational skills that he urged him to go into politics. "The country needs young men like you in the leadership of the nation," Baskin said.
The young Klan leader went on to become one of the most powerful and enduring figures in modern Senate history.
A Senator's Shame
Here is a bit more,:
On June 10, 1964, Everett Dirksen (R-IL), the Republican Leader in the U.S. Senate, condemned the Democrats 57-day filibuster against the 1964 Civil Rights Act. Leading the Democrats in their opposition to civil rights for African-Americans was Senator Robert Byrd (D-WV). Byrd, who got into politics as a recruiter for the Ku Klux Klan, spoke against the bill for fourteen straight hours. Democrats still call Robert Byrd the conscience of the Senate.
In his speech, Senator Dirksen called on the Democrats to end their filibuster and accept racial equality.
Everett Dirksen and the 1964 Civil Rights Act
Next, we can go even further back in history to 1866, where a Democratic campaign poster such as this one was circulated:
So yeah, Republicans get the credit here. They advocated Civil Rights, while Democrats did not.