IOTL, most presidents have been governors or senators. Your challenge is to, with no POD before 4 March 1881, have more presidents elected directly from the House of Representatives, and/or even have at least one president who has only been mayor or in some other "lower" office before being elected president. Military officials do not count; people with no experience in elected office do.
However, nothing after, say, 1972. So no Perot, no Giuliani, no Bloomberg, etc.