Warren Harding is usually considered one of the worst US Presidents in the surveys of history professors that /u/itsallfolklore discusses here. Though, of course, there are historians whose take on Harding diverges from this consensus.
There are a variety of reasons why Harding's reputation is so poor - namely, the perception that he was something of a puppet, the personal scandals associated with Harding that emerged after his death, the political scandal of the Teapot Dome being the first time a Cabinet member had gone to prison, and Harding not really having signature policy achievements beyond a somewhat nebulous 'return to normalcy'.
Firstly, the perception of Harding for a long time, until the 1960s, was that he was a small-town newspaperman plucked from obscurity by men in the archetypal smoke-filled room for his good looks, his genial manner, and his basic lack of interest in actually running the country. His public perception was perhaps similar to the public perception of George W. Bush in the 2000s, when people assumed he was something of a puppet of Dick Cheney without much depth. The Harding family kept the Hardings' letters and correspondence private until the 1960s, which meant that this was the dominant perception of Harding for close to half a century (the private papers made it clearer that Harding had a lot more influence on policy direction than had previously been thought, and that he was more articulate on policy matters in private).
Secondly, a number of lurid details were published about Harding relatively soon after his death in 1923, which further fixed public views about him for some time. Firstly, in 1927, Nan Britton released a book called The President's Daughter in which she claimed that her illegitimate daughter's father was in fact Harding. In a more socially conservative age, this claim did a lot of damage to Harding's reputation amongst conservatives, though its veracity was in dispute until 2015, when DNA testing showed that it was true. Secondly, a 1930 book by Gaston Means, who had worked at the Bureau of Investigation (but who Coffey calls a 'charlatan' and 'swindler') claimed not only that this was true but that Means had even confirmed this to Florence Harding (Harding's wife), who had promptly poisoned her husband. Florence had died in 1924, and was not around to deny such things, and the Harding family keeping their papers private until the 1960s meant that they could not shed light on these rumours one way or the other.
Thirdly, a lot of the public was inclined to believe such claims because of the Teapot Dome scandal, which painted Harding in a poor light - his Secretary of the Interior Albert Bacon Fall was the first ever Cabinet member to go to prison, for his part in taking bribes to lease government-controlled oil reserves to oilmen (including at Teapot Dome in Wyoming, thus the name of the scandal) at low rates. Even a basically positive biography of Harding like 1969's The Harding Era by Robert K. Murray finds that there were several character flaws of Harding's which directly led to the Teapot Dome scandal (Murray pushes hard against the small-town newspaperman plucked to power by the smoke-filled room thing, but even he ultimately sees Harding as unfit for the Presidency, temperament-wise).
As to Harding's policies, the defining 'brand' of Harding's presidency was the 'return to normalcy'. Phillip G. Payne claims that
it was not the case that Harding was a polarizing figure while president whose policies were vigorously debated, indeed it was just the opposite: there are few policy debates from the Harding years.
It's difficult to put modern political labels of progressive and conservative on the political parties of the time, but there were certainly progressive movements in the early 20th century, and Harding was decidedly in contrast to the progressive, statist values of Woodrow Wilson that, by 1920, were seen poorly by the public. Harding's big brand was the 'return to normalcy', and his stance was a sort of return to the 'small government' values of the Gilded Age. These kinds of policies continued throughout the 1920s and early 1930s under Coolidge and Hoover, and they seemed to be unable to deal with the Great Depression, especially once Franklin Delano Roosevelt's Keynesian New Deal policies became the basis of essentially bipartisan policy until Reagan. Insofar as Harding's policies were perceived as playing a role in leading to the Great Depression, perhaps unsurprisingly they were received poorly by historians, especially left-leaning ones. And insofar as there were few policy debates from the relatively-shortlived Harding years, and so there was little in the way of big ideas and strong stances for historians to discuss, Harding's lack of policy prowess means that there aren't a huge amount of strong defenders of his legacy. It's perhaps indicative that the most positive portrayal of Harding comes from a 2004 biography by John Dean, who, well, also happens to be a person went to prison for his role in Watergate.
Sources:
'Progressivism in an Age of Normalcy: Women’s Rights, Civil Service, Veterans’ Benefits, and Child Welfare' by John F. Fox, Jr in Katherine Sibley's (ed.) A Companion to Warren G. Harding, Calvin Coolidge, and Herbert Hoover
'Harding Biographies' by Justin P. Coffey in Katherine Sibley's (ed.) A Companion to Warren G. Harding, Calvin Coolidge, and Herbert Hoover
'The Harding Presidency: Scandals, Legacy, and Memory' by Phillip G. Payne in Katherine Sibley's (ed.) A Companion to Warren G. Harding, Calvin Coolidge, and Herbert Hoover