They already have a solution for this already implemented. If you're not a citizen, you have to carry identification that shows you are allowed to be here. It's what is called your green card (though it's not green). Not carrying it is already punishable by anything from a hefty fee to deportation. All legal immigrants already know this. Citizens (naturalized or not) do not need to carry papers (yet).
If they can read a driver's license, they can read a green card.