I never carry any identity documents. I know I should, but, as has been said, you are also advised not to take your passport with you. I could compromise by taking my driving licence, but life is too short!
I always regard these polls with suspicious ion. I recall reading that there were terrible immigration queues at Incheon, for example. Also, I find Charles de Gaulle a mess. I'm surprised that any US airport is anywhere near the top!