Illegal aliens are an infestation so I don’t see the problem with calling them cockroaches. Besides, it is rather apt. The amnesty crowd loves them until they have to come home with them.
I’ve always broken down people into groups when I’m talking about immigration:
Ants - the people that are productive citizens that set up colonies (civilizations and cities) and keep them properly maintained.
Termites - the people that move in to the Ant’s colonies and don’t maintain them. They rot and destroy them from within and perform little or nomaintenance.
Cockroaches - the people that move in after the Termites have done their damage and feed on the leftovers after the Termites have moved on to the next colony to destroy.