Harding is the worst in terms of professional competence. However, when we say "bad" president, we must also factor in the impact of the president's actions on the country and the world. In the early twenties, the US economy was booming and the country retracted from international affairs. The economy ran on auto-pilot and Harding's incompetence had little lasting effect. Likewise, Coolidge could sleep his days away with little consequence.
Had JFK started a nuclear conflict, he would have been condemned. Since he did not, he is remembered as the hero who invigorated the space program, presided during the Berlin crisis, started a war on poverty, started the Peace Corps, met with Martin Luther King to discuss civil rights, established physical fitness programs in schools, and yes, turned the Russians away from Cuba.
No twentieth century president ended up putting the integrity of the US in jeopardy. It will take decades, though, for the impact of GW Bush's decision to invade Iraq to complete its impact on world history. When all is said and done, I really believe the GW Bush administration will go down as the worst since 1900.
And Hurricane Katrina is a black eye on the Bush administration. It is not micro-management for the president to take immediate action on an event of this magnitude. The US military is the only institution large enough to move in for the immediate assistance needed. It would be four days before military helicopters would arrive on site. By contrast, it took only three days for our copters to assist earthquake victims in Pakistan.
Assistance from the Mexican Army and Canadian Red Cross reached New Orleans before that of the US military. Pathetic.