I carry my passport with me at all times. I did it even when I was living in the States. A habit, I suppose, from having lived outside the US for so many years. Though, when I was in the US full time, I usually carried my EXPIRED passport, which I could lose without crying
I am a 3rd generation Irish-American (but since I have an Hispanic last name now, I worry) and I find this Arizona law to be Draconian at best. I just don't see how it's not going to be struck down in the federal courts.