Cristina Rodriguez makes some points I mostly agree with.
The vast majority of Americans recognize that the 12 million undocumented immigrants cannot simply be found and shipped out, both for the sake of the American economy and because it is unfair to many that have worked and raised family in America.
Imagine if we could know everyone that drove above the speed limit in the last ten years and then decided to give them tickets. It would be an absurd result with the majority of Americans owing hundreds of thousands of dollars; their license revokes many times over. It is simply unfair to set up a particular enforcement scheme (or lack of enforcement scheme) and then attempt to harshly punish those who acted in response to that system.
It appears that the current system is a dysfunctional stalemate between business interest that want more immigrant workers and pro-immigrant groups and the know-nothing nativists. The easiest thing for a politician to do is keep official immigration low, by restricting official immigration, but keep unofficial immigration high. Similarly, politicians can get behind a big wall. Like low visa numbers, it looks like an effort to reduce immigration, but it is unlikely to significantly limit the number of undocumented workers.
I would propose a massive increase in the number of legal immigrants along with punishment largely directed at employers who hire illegal immigrants or do not comply with labor laws.