The only time the Senate used a filibuster to prevent a Supreme Court nomination from being voted on was 1968. On a nominee--by a lame-duck President--who clearly had ethical problems, Abe Fortas:
In June 1968, Chief Justice Earl Warren informed President Lyndon Johnson that he planned to retire from the Supreme Court. Concern that Richard Nixon might win the presidency later that year and get to choose his successor dictated Warren's timing.
....To replace Warren, he nominated Associate Justice Abe Fortas, his longtime confidant. ....
A seasoned Senate vote-counter, Johnson concluded that despite filibuster warnings he just barely had the support to confirm Fortas. ....Johnson urged Senate leaders to waste no time in convening Fortas' confirmation hearings.
Responding to staff assurances of Dirksen's continued support, Johnson told an aide, "Just take my word for it. I know [Dirksen]. I know the Senate. If they get this thing drug out very long, we're going to get beat. Dirksen will leave us."
....Those hearings reinforced what some senators already knew about the nominee. As a sitting justice, he regularly attended White House staff meetings; he briefed the president on secret Court deliberations; and, on behalf of the president, he pressured senators who opposed the war in Vietnam. When the Judiciary Committee revealed that Fortas received a privately funded stipend, equivalent to 40 percent of his Court salary, to teach an American University summer course, Dirksen and others withdrew their support. Although the committee recommended confirmation, floor consideration sparked the first filibuster in Senate history on a Supreme Court nomination.
On October 1, 1968, the Senate failed to invoke cloture. Johnson then withdrew the nomination, privately observing that if he had another term, "the Fortas appointment would have been different."