Eeerrhhh. Tap tap tap.
Like many of the grammar things that seem to come up on here, it’s not so much right and wrong, but rather word choice can convey a very specific meaning.
“there’s a little Irish in all of us” could be taken to imply that the qualities herein associated with being Irish (joyousness, friendliness, etc.) are only present when in a large group (all of us)… but if each of us went off to a distant corner we wouldn’t have “a little Irish” present.
If that’s indeed the case, then there’s only “a little Irish” in the group.