A slogan from the 1964 Presidential campaign of Democrat Lyndon Johnson. It referred to opponent Barry Goldwater's own slogan, "In Your Heart You Know He's Right."
Grzcyrgba says re: In your guts you know he's nuts, it might be worth noting that the slogan may have been coined by Bill Moyers, who was a campaign aide to Lyndon Johnson. Apparently Johnson also used "In your heart, you know he might" (i.e. start World War III). It wasn't the nicest of campaigns.