Is a president "worse" or "worst" because he was incapable of handling the demands of the office - or because he presented a clear and present danger to the Republic and its Constitution?
Carter and Ford were clearly in over their heads. To be fair, they were presented with formidable inflation and unprecedented energy shortages. Worse.
Nixon was the last liberal president. Check out the accomplishments of his administration. He had a serious psychological disorder which set him up for his posse to do him in. Worst.
From what I know of Harding's inclinations they were somewhat progressive. Some of his appointees went to prison. Harding, for all we know was honest with the people's money. I don't think ANY 20th Century presidents screwed around as much as JFK and Woodrow Wilson.
The worst president EVER was Franklin Pierce - but Generalissimo W. Bunnypants probably has him beat. Pierce had an excuse - he was a drunk...