Green’s Dictionary of Slang

terrier n.

[? the dog (small, tough, unrelenting, known as the ‘daredevil’ of the canine world), or the Irish-American folk song ‘Drill Ye Tarriers, Drill’ composed in 1888by the comedy duo (Thomas) Casey & (Charles) Connolly and referring to mid-19C Irish labourers building the railroads]

(US und.) an Irish person.

[US]W.G. Davenport Butte & Montana Beneath the X-Ray 70: Go into any Irish saloon in Butte any day of the year when there is a bunch of Irish terriers slopping up.
[US]‘The Lang. of Crooks’ in Wash. Post 20 June 4/1: [paraphrasing J. Sullivan] The Irish race [has] numerous cognomens, as a boiled dinner, harp or a mick, also a terrier.