1860 Census Data
The first reference to a recognizable family member in the US census data appears in 1860, when a Cornelius or Connel Haggerty (“Cornel” on the form) appears in Northeastern Pennsylvania. He is 33, born in Ireland (c. 1827), and working as a miner in Tamaqua, Rush Township, Schuylkill County, PA, about 10 miles south of Honey Brook. He is living with his Irish-born wife Margaret and their 3 children, all born in Pennsylvania: Mary 6, James 4, and Michael 2.
It is unclear whether James J. Haggerty is in the US at this time; I found no sign of him in the 1860 census.