Sorry, but the 1964 civil rights act wouldn't have passed if not for the republicans. More repubicans voted for all 3 (civil acts rights of 1964, voting rights of 1965, and fair housing bill of 1968) than the democrats. If the democrats were the majority of both houses of congress none of these would have passed.
Civil rights bill ---
80% house republicans to 63% democrats
82% senate republicans to 69% democrats
80% of Republicans in the House and Senate voted for the bill. Less than 70% of Democrats did. Indeed, Minority Leader Republican Everett Dirksen led the fight to end the filibuster. Meanwhile, Democrats such as Richard Russell of Georgia and Strom Thurmond of South Carolina tried as hard as they could to sustain a filibuster.