Yes, there should be a national ID -- but, it should be in form of a national health insurance/single payer card, similar to the one in Canada. It can be effectively swiped at hospitals for instant access to medical recorRAB.

In this case, it could also be used to verify employment.

And yes, employers should be heavily penalized for hiring illegal workers who should be humanely, which also means swiftly, returned to their homelanRAB.