I would assume the president with the least authority in opinion polls is Nixon, probably because it is freshest in people's minds. There is also Herbert Hoover who will always be blamed for the Great Depression even though it was totally beyond his control (it started in Europe and there was nothing that could be done), and Hoover's policies, not FDR's, were what eventually ended the Depression.
IMHO the worst presidents were probably Grant and Harding, both of their administrations were totally corrupt and scandal ridden (yeah I know they're both Republicans, but it's the truth).
In modern times, Carter was certainly the worst president (he was so much less effective than Clinton), he made a laughing stock of the country and his failures are entirely responsible for the groundwork of our present-day troubles with the jihadists.
In my opinion, Clinton was the very worst president ever elected. A couple of years ago I read every Inaugural Address given by every president. Everyone of them, except for Clinton, thanked the people with varying degrees of humility, for having voted for them. The greater the president, the more humble they were. Clinton did not acknowledge the people in any way, but instead I came away thinking that he was so puffed up with himself that their was no room to be the least bit humble. Not only was he not humble, but just previous to giving his Inaugural Address he began his 'presidency of lies' by lying to God. No other president did that, intending to decieve from the get-go. Which, by the way, lying is why Clinton was impeached.
There was an interesting poll taken while Clinton was in office which put Bill and Hillary in the top 5 with Hitler, Stalin and Pol Pot as the most evil people of the 20th century. Compare that poll with this poll where Clinton comes in next to last. No other American president made it to the top ten of that 'evil' list.