Curious about this one myself.
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.