I had a look at the table provided here:
http://factfinder.census.gov/servlet/QTTable?_bm=y&-qr_name=DEC_2000_SF3_U_QTP13&-geo_id=01000US&-ds_name=DEC_2000_SF3_U&-_lang=en&-redoLog=false&-_sse=on
It seems that if I add "British", "American", "Scottish", "Welsh", "Irish", "Scots-Irish", "English", and unspecified ancestry (adjusting it by probability that they are German or Italian ancestry) together, it seems not more than 35% of all Americans have majority British/Irish ancestry. Not sure if my guess proves correct.
I know that there were a large number of Welsh in my states (Michigan) upper penninsula at one time. Mostly miners from what I can find. I live in an area called the Irish hills, so I'm assuming there was a fair sized Irish population here. I'm German and grew up in a town named after Hanover Germany.
We were a pretty diverse european bunch here.
Out of a total U.S. population of 281.4 million as of the 2000 census, about 115.1 million Americans have roots in the British Isles, assuming those that did not identify their national origin were equally distributed among the population.