It is believed that, at the time of the Revolution, they comprised 10-15% of the population of the United States. Their negative feelings toward England played no small part in the emotion of the "stew" that led to the American Revolution.
Although there is evidence of the use of this term, or others, (Ulster Irish, Northern Irish, Irish Presbyterians) to differentiate the Scotch/Irish immigrants from other citizens of America, it is believed to have generally fallen into non-use by the 1840's, wherever it had been used. The use of the term "Irish" in the United States up to that time usually meant Scotch-Irish, as the Catholic Irish simply had not been a major immigrating force until that time.
All that changed, however, with the potato famine and the resulting crunch of the greatest immigration America has ever experienced, from the southern regions of Ireland. An estimated 2 million Irishmen, mostly Catholic, and mostly from the southern parts of Ireland, immigrated to America during the period 1846-1856. They were poor. They congregated in the cities in which they landed in ghetto clusters. They were Catholic. They would work for next to nothing while native born American workers saw jobs threatened and the decline of value in their own labor. The Irish, as many new classes of immigrants are in a new country, were not looked on favorably by the general population.
This caused a renewal in the resident population of Scotch-Irish Americans to identify themselves in such a manner that they would not be thrown in the same "class" of citizenry as the new, Catholic, Irish immigrants. Thus, a renewal in the use of the term Scotch-Irish.
It is a useful term to the family historian as the Scotch-Irish people are definitely a different class of immigrant than the southern, Catholic Irish; nor, can they be thrown in the same pot as their Scottish brethren. "..the Scots who lived in Ulster before they came to America simply were not, in background, religion, and many other aspects of culture, identical with the Irish of the southern provinces of Leinster, Munster, and Connaught; neither were they, after many decades, any longer identical with the people of Scotland." The Scotch-Irish, A Social History, pg. 333 - James G. Leyburn.