Dear Jeanne,
In 1860 there is an Abram Bronson, age 25, in the household of Reuben Bronson, age 43, in Adams, Lasalle County, Illinois. Listed after Abram is Mary Bronson, age 23, and Charles, age 1.
Reuben was born in New York, as was Abram. Possibly Abram's brother - if you can find a marriage record for Reuben, it may have his parents' names.
Hope this helps. -NGP