Anything is possible. Congress and the States might even get together and amend the Constitution to make such a law constitutional.
The question is - who will enforce it? Some State Constitutions protect the right to keep and bear arms explicitly. The Federal Government doesn't have enough employees, so they would, theoretically, order the States to do their work. Most of the states, even the liberal ones, don't have enough employees that they would feel safe.
Worst case scenario - guns would be like illegal drugs, illegal immigrants, and rich liberals cheating on their taxes - technically illegal but nothing gets done about it. Nobody has enough money to keep violent repeat offenders locked up; rapists and murderers get released to rape and kill again. It would take a serious adjustment in priorities for the US to prioritize punishing gun owners over drug dealers.