Cleveland was still a bachelor when he ran for President. There is some uncertainty whether he was really the father of the illegitimate child. Apparently the mother had had affairs with several men but the others were all married so Cleveland agreed to take responsibility. I think the child later grew up to be a doctor. It would be interesting to find a descendant and do a DNA test to determine whether Cleveland was really the father.
Apparently James G. Blaine's first child was born three months after their wedding.
I had the benefit of a great history teacher in high school, which I think is where I learned the jingle. I know for sure he told us about Ma, Ma, Where’s my Pa, and the Democrats’ rejoinder, as well as “Rum, Romanism and Rebellion”.