This is ironic since Harding was also rumoured (not convincingly) to have been in the Klan. Lotta that going around at the time -- both the Klan and the rumors.
In the NYT link:
>> By 1920, when Harding was running for president as the Republican nominee, William Estabrook Chancellor, a professor at the College of Wooster and a racist supporter of the Democratic president, Woodrow Wilson, collected unsubstantiated statements from various Ohio residents asserting that Harding had black ancestors. The research was then published in pamphlets that were distributed to voters. <<
Harding wasn't running against Wilson anyway, and by 1920 Wilson was so despised that Harding barely had to campaign at all, winning the biggest landslide to date against Wilson's coattails (much like McCain had no shot in 2008 carrying the Bush baggage).
Rumors of African ancestry in 1920 would have been quite a bit more powerful in that period of the nadir of racism in this country but obviously they had little if any effect.
Actually as far as "blackness", if it even matters, there's a better case to be made for Lincoln.