Does Anyone Know of a Jane Sherman Cousin to William T Sherman and Senator Sherman

Jane was born (supposedly) in 1826 in Ephratah New York. In 1847, she married Thompson Daniels and had 7 children. She died in childbirth in 1863 with her last child in (according to my calculations) Elkhart, Indiana.

Jane is my 3rd great grandmother. I haven't been able to figure out who her parents were. I've been stuck at this brick wall for 3 years now.

Any help or information would be greatly appreciated!

Pam