How unkind of you not to mention who you thought her ancestors were. That can cause an expert to waste hours of time pursuing a wild goose chase. It's like being asked to search for Wilson Reagan with no other information. However, in this case, it isn't a wild goose chase, and there aren't any Native Americans in the family tree.
In any event, here is the 1870 census for Burns, La Crosse, Co., WI
William Balch 45 M Farmer b VT
Adeline Balch 29 F b NY
Alda Balch 19 F b WI
Francis Elmer Balch 6 M b WI
Willie Balch 3 M b WI
Ida Balch 2/12 F b WI
1860 Census - Sparta, Monroe Co., WI
William Balch 35 M Farmer b NY
Adaline Balch 19F
Clara A. Balch 6/12 b WI.
Evidently William Elmer Balch and Adaline XXXXX XXXXX were married in Wisconsin about 1859/60. The records are not available online.
Adaline/Adeline XXXXX XXXXX was the daughter of Albert W. Smith b 1817 Steuben Co., NY d 1895 Richland, WI and his wife Henrietta Swartout b 1820 Steuben Co., NY d 1849 Portage, WI. The Swartouts are of Dutch ancestry. The remainder were English.