Well, this is an example of the motte and bailey technique. (
http://rationalwiki.org/wiki/Motte_and_bailey)
When most people think of Nazis, they think of concentration camps and mass murder, not totalitarianism. That's the image and idea they want to associate with a group of people when they accuse them of being Nazis, and to argue otherwise would be disingenuous.
For example, you could argue that people who advocate for smoking bans and vegetarianism are Nazis and literally Hitler, as they too tried to reduce the amount of smoking and meat consumption in the name of public health.
Then when they get called on logical inconsistencies (because somebody is against smoking doesn't make them a Nazi) they retreat to a different, more easily defensible assertion.
Also, I don't see xenophobia in any of this discussion. They want rigorously enforced immigration laws, which are already on the books.
The executive branch is in charge of law enforcement, and I don't see how that is xenophobia when you're targeting illegal immigrants, rather than people of a specific ethnic group.