The main "evidence" referenced in the historical literature is three fold:
First, the NINA myth was so convincing that the Irish saw no need to investigate further, or to document the discrimination, or to set up a protective organization. (They of course organized extensively, in both Ireland and America, to protest maltreatment back in Ireland.)
Second, historians point to contemporaries who commented unfavorably on the Irish, generalizing from a handful of cases to create a stereotype of the dominant views of all of American society. Now indeed the 19th century literature is filled with eyewitness and statistical descriptions of Irish drunkenness, crime, violence, poverty, extortion, insanity, ignorance, political corruption and lawless behavior. The reports come from many cities, from Catholics and non-Catholics, social scientists and journalists, Irish and non-Irish. The question is not whether the Irish were admired. (They were not.) The argument that the dominant popular stereotypes of the Irish were especially nasty does not hold up under careful examination. There is no evidence that more than one in a thousand Americans considered the Irish as racially inferior, non-white or ape-like...
The NINA slogan was in the mind's eye, conjured by an enormously popular song from 1862. Job discrimination by the Other was too well known to the Irish to need evidence beyond NINA, or the "recent" burning of the Ursuline convent. Historians engaging in cultural studies must beware the trap that privileges evidence derived from the protests of self-proclaimed victims. Practically every ethnoreligious group in America cherishes its martyrs and warns its members that outsiders "discriminate" against them, or would if they had the opportunity. The NINA slogan had the effect of reinforcing political, social and religious solidarity. It had a major economic role as well, strengthening the politicized work-gang outlook of Irish workers who had to stick together at all times. It warned the Irish against looking for jobs outside their community, and it explained away their low individual rates of upward social mobility. The slogan identified an enemy to blame, and justified bully behavior on the city streets. NINA signs never faded away, even as the Irish prospered and discrimination vanished—they remained a myth about origins that could not be abandoned.