Wow I was surprised by this figure, so I tried to find the source everyone quotes. It appears to be a 2006 telephone survey of 987 randomly-selected voting age citizens that were then weighted for an underrepresentation of race (so perhaps not that accurate). Anecdotally, I work in a safety net hospital and it is really rare for someone to come in without ID, which is why those numbers seemed so surprising to me...

https://www.brennancenter.org/media/6697/download

I could easily have missed a better or more recent study, so if anyone has one please post it!