I read in Arthur Schlesinger's book, The Disuniting of America, that Ishmael Reed had written that if Alex Haley, author of Roots, had “traced his father’s rather than his mother’s bloodline, ‘he would have traveled 12 generations back to, not Gambia, but Ireland’.”
Apparently this is true of Barack Obama, too. Erin O'Connor writes on Critical Mass that
There are far more Irish people living outside of Ireland than in it — the famine, and the hard decades afterward, meant that for many years Ireland's population shrank rather than grew, despite the country's historically high birth rate. They say there are more than 40 million Americans of Irish descent (compare that to today's Irish population of about 4,000,000, a quarter of whom live in Dublin). When you get to talking to people about their ancestry, as I like to do, it sometimes seems as if just about everyone has some ancestor who came from a remote Irish village ("remote" being, in this phrasing, utterly redundant). So I wasn't surprised to find out that Barack Obama is Irish, too.[Tiny Irish Village Is Latest Place to Claim Obama as Its Own By Mary Jordan Washington Post , May 13, 2007]
Obama's great-great-great maternal grandfather was a shoemaker in Moneygall, County Offaly before he emigrated to the U.S. in 1850, hard on the heels of the famine. No word on whether Obama finds this information thrilling.
Probably not. He's not, after all a position to become the first Irish President. Out of the variety of ethnic and national identities he could choose to identify with, Irish-American will be low on the list.