Lyndon Johnson nearly changed his mind and ran for re-election in 1968 at the 11th hour, according to declassified audio tapes. Seeing on TV the Democratic party's chaotic convention in Chicago—where a massive police force clashed with anti-war protesters—the president feared that delegates would reject his Vietnam-war policy and chosen successor, Hubert Humphrey. So he called convention staff and discussed a plan to helicopter in and run for the nomination himself, the Daily Mail reports.
But LBJ scuttled the plan when the Secret Service said they might not be able protect him. A worthy side-note: Johnson also called Chicago Mayor Richard Daley to congratulate him on his handling of the protesters, the BBC reports. The BBC details another story that got some press a few years ago—about Johnson knowing of Richard Nixon's undermining of Vietnam peace talks in 1968. But Johnson kept quiet, fearing that it would lead to revelations that the FBI had been bugging the South Vietnamese ambassador's phone, and cause a bigger national security scandal.