In 1966, Cooper again won re-election over John Y. Brown, Sr., by 217,000 votes, breaking his own record of largest victory margin for a Kentucky senatorial candidate, and carrying the vote of 110 of Kentucky's 120 counties. In the lead-up to the 1968 Republican presidential primary, he endorsed New York Governor Nelson A. Rockefeller, saying that Americans would only support a candidate who took a clear position on Vietnam. Rockefeller had laid out a plan for reversing the Americanization of the war, while other Republican candidates tried to remain non-specific about how they would handle it. As Rockefeller's candidacy faded, Cooper encouraged his colleague, Kentucky Senator Thruston B. Morton, to seek the presidency, but Morton declined. The nomination – and eventually, the presidency – went to Republican Richard Nixon.