They won't make VPNs illegal, because that would be absolute lunacy that would be mocked along the lines of Senator Ted "series of tubes" Stevens.
What they will do is have the Department of Justice sue the large VPN providers into oblivion for conspiring to enable mass copyright violation or some shit, highlighting their refusal to block these sites that a federal judge has determined should be blocked under this law. This is the first domino that allows them to have a legal crack at the VPN providers, which is what the media industry really wants crushed.
Corporate VPNs and site-to-site tunnels will still be just fine.