According to a recent New York Times article, it was probably not pneumonia.
In those days the nation’s capital had no sewer system. Until 1850, some sewage simply flowed onto public grounds a short distance from the White House, where it stagnated and formed a marsh; the White House water supply was just seven blocks downstream of a depository for “night soil,” hauled there each day at government expense.
That field of human excrement would have been a breeding ground for two deadly bacteria, Salmonella typhi and S. paratyphi, the causes of typhoid and paratyphoid fever — also known as enteric fever, for their devastating effect on the gastrointestinal system. . . .
Harrison had a history of dyspepsia, or indigestion, which potentially heightened his risk of infection by gastrointestinal pathogens that might have found their way into the White House water supply.
Whatever killed him, mommas, don’t let your babies grow up to be Whig presidents unless you want them to die in office.