It's been awhile since you asked your question, hopefully you'll get this message. Sorry, I don't check the messageboards as often as I should.
I checked the 1910 Gem County census for Francis Dresser. Hopefully enough details will be available so that you can determine whether he is the man you are looking for. He was born in Canada but his parents were from Vermont. His wife's name is Harriet and she was born in Pennsylvania. It looks like he has a son, Leonard, born about 1874 in Iowa, and a daughter, Cora, born about 1865 in Iowa. From the age of his grand-daughter, it looks like they were probably in Iowa during the years that you mention he was supposed to be mayor in Rochelle, but not necessarily.