He served as a member of (among other committees) the powerful Senate Foreign Relations Committee. McCarthy became known to a larger audience in 1960 when he supported twice-defeated presidential candidate Adlai Stevenson for the Democratic nomination. He pleaded during his speech, "Do not reject this man who made us all proud to be called Democrats!" He joked about his own merits as a candidate, "I'm twice as liberal as Hubert Humphrey, twice as intelligent as Stuart Symington, and twice as Catholic as Jack Kennedy." He was considered as a possible running mate for Lyndon Johnson in 1964, only to see fellow Minnesota Senator Humphrey chosen for that position.