There is no North American or US accent. I mean keep in mind:
Landmass of Ireland: 32,595 sq mi
Landmass of the European Union: 1,707,642 sq mi
Landmass of the United States: 3,531,905 sq mi (The Lower 48 ALONE are 2,959,064 sq mi)
The United States is absolutely gigantic. Think of how many dialects and accents are in the British Isles. Same applies, though far more spead out. Georgia sounds different from much of deep Alabama which sounds different from Virginia which sounds different from Ohio which sounds different from Boston which sounds different from Jersey and so on.
Having said that, Scotts-Irish descendants may have similarities in some areas in the country.
I'd say though that the differences between American accents tend to not be as different as depicted, especially with the media and internet which I believe is converging dialects. For example, I live in Canada but pronounce many words the American way due to the influence of media.