I say this as someone who would strongly support a federal mandatory national ID system (and the ACLU, generally)
Oh, I doubt it's a left-right thing. I'm pretty lefty these days, and I oppose a national ID. Some minority groups, like say Jewish folks, might carry bad connotations about putting everybody in a big database so we can keep track of (and categorize) them.
But, of course, there's not much preventing the local government from sharing the info with the Feds.
It's something so unlikely to come up in day-to-day interactions that it's not really that important. I'm sure if I got stopped in, say, France, and had no passport to show, they wouldn't exactly lock me up on the spot, they'd find a way to accommodate me.
I still only have a really vague understanding of what happens if a cop in the US wants me to identify myself and I refuse. If I'm not suspected of a crime, obviously, I can just walk away. I'm not really sure what I'd do if I was arrested for cause and refused to identify myself.