Hello,

There is a JAS. BURCHAM in the 1880 census of OH, Lawrence Co., Windsor T.

Jas. Burcham age 47 farmer b. OH Father b. KY; mother b. VA
He is married to
Abagail Burcham age 41 b. OH; Father VA; mother: OH
children:
There is a name that cannot be figured out; even Ancestry.com
has him as just Burcham. It could be William age 20 and listed as son
Mary A age 13 dau. b. OH
Oliver G. age 3 son b. OH

I know this family does not have the names you state in your message. Also the ages for James and Abigail are older in the census.

Jewel Callicoat Cabana in her book has this family listed as:

JAMES L. BURCHAM, son of JOHN FRANCIS BURCHAM SR, married ABIGAIL DILLON, daughter of PETER DILLON. They had one child:
SARAH 'SALLIE" ELIZABETH BURCHAM who married JAMES A. BIAS.

Do you think this is the family for which you are looking?
If not, let me know and I will search some more.
Helen