Hell, no. Secure the border. It's not that hard to do. No reason citizens should have to prove their legitimacy to anyone.
Sure secure the border. But how are you going to deal with the scofflaws that are already in the country? Are you just going to start rounding up folks with brown skin like me? Of course not. We already require folks provide proof of citizenship for a host of things. Why not make an ID that cannot be forged and require that it be presented when one gets employed in the US?