Up until 1910, no records of mother tongues were kept so it is unfortunately impossible to be exactly sure of the extent of Irish-speakers prior to the early 20th century. Nevertheless, it is generally accepted that somewhere between 20 and 25% of the eight million people who left Ireland between 1801 and 1922 were monoglot or bilingual Irish-speakers.
This response is in relation to the second half of the nineteenth-century, following the Famine emigration. This is a useful period to assess the emigration of Irish-speakers as not only was it a peak period of emigration, but also occurred before the Gaelic Revival (c.1890-1920) which completely changed attitudes towards the language and created an identity separate from the traditional language community.
The Irish language was far more common in the US at this time than is generally considered but the prevalence of bilingualism in Ireland in the 19th century has led to the assumption that English was the language of choice for emigrants and that Irish just ceased to be spoken immediately upon arrival. This is not the case, though, and there is evidence of Irish continuing to be spoken as a vernacular in many regions in the US, though mostly on the east coast, such as priests hearing confessions in Irish, of monoglot speakers requiring interpreters in the courts, and of groups of workers speaking Irish with one another (for example on the docks in Philadelphia). The language did not disappear but simply retreated below the surface of society and became a language of the home, and was not taught to subsequent generations.
Unfortunately, establishing exact numbers of Irish-speakers (monolingual or bilingual) is next to impossible. There is no statistical information available - it was not until 1910 that census-takers in the US began to record the mother tongue of anyone born outside of the United States, as well as that of any foreign-born parent of those recorded in the census. Also, Irish was a predominantly oral language which left only minimal written evidence, and its speakers, if literate, are generally understood to have been so in English rather than Irish, largely as a result of the National School System (established in Ireland in 1831). Minority languages tend to evade the historical record.
As a result of this, the 20-25% statistic is largely based on immigrant backgrounds. The emigrant stream in the post-Famine period was mostly comprised of Catholic labourers from the west of Ireland, where Irish continued to be the primary language for between 50 and 80% of the population, based on Irish census returns for 1841 and 1851. Because these areas also had the highest rates of emigration post-1845, it is inferred that a certain number of Irish-speakers must have emigrated. This, combined with anecdotal evidence, proves that there were Irish speakers in the US but exact numbers are impossible to provide.
Canada, on the other hand, had Irish-speaking communities well into the 20th century.
References:
Karen Corrigan in Patrick O' Sullivan (ed.), The Irish in the New Communities (1992)
Dennis Clark, ‘Muted heritage: Gaelic in an American city’, Éire-Ireland 6, 1 (1971)
Nicholas Wolf, Irish Speakers & the Empire City http://www.nyuirish.net/irishlanguagehistory/
Thomas Ihde, The Irish Language in the United States: An Historical, Sociolinguistic and Applied Linguistic Survey (1994)
Ofelia García and Joshua A. Fishman (eds), The multilingual apple: Languages in New York City (1997)
Maybe a silly question, but I'm genuinely curious: is the Irish language you're speaking of here equivalent to Gaelic? Because I always thought of the predominant language of Ireland being English.
Edit: thank you for the responses! This is enlightening. For whatever reason I had always thought the vast majority of people in Ireland always spoke English for the past few centuries.