We already have a national ID of sorts, but you are incorrect. Americans are not required by law to carry their papers. The courts have ruled on this in numerous cases. but that doesn't stopped people like you who are advocates of fascism, or susceptible to fascism, from advocating a fascist policy time and time again
Not your papers, your state issued DL or ID card. That is a law in all 50 states, rarely enforced thanks to online DMV and NCIC capabilities. It's not a federal law, its a state law in all 50 states. Prior to everything being computerized, a cop wouldn't know if a person had a valid DL without it being present, and cops couldn't tell if a person was a fugitive without ID, so DMV's issued ID cards in the absence of a DL if a person was ineligible. Today, the online NCIC and DMV allows cops to run a name and DOB check to ID any citizen without an ID, so it's basically a law that is not really necessary, but still IS ON THE BOOKS in all 50 states.
I promise if you get pulled over, the cop will verify your identity if you don't have a DL or ID card on you. But you had to be issued one, as all people are, whether they know it or not, through their state ID by virtue of having a social security number. It's called a "customer number" in most states, so if you drive drunk without a valid DL, you have a number they can "suspend" for punishment so if you get caught again you can be subject to the Driving Under Suspension 2nd offense statute. A non-citizen won't be in this ID system, because they have no DL or no social security number, THUS the federal law requiring them to "have their papers" on them at all times.
I'm not advocating or criticizing this set of laws, I'm informing the lefties that every person, like it or not, is verified through some type of "papers", be it physical or electronic.