You Americans need to understand just how much is at stake here. We are in the early stages of a world war with Islam, Muslims are working to get nuclear weapons and are openly calling for the physical destruction of the West. Your enemies are watching the way you are handling the illegal situation, and they are not impressed. Do you think the North Koreans or the Iranians are scared of a country that allows itself to be intimidated and held hostage by a bunch of Mexicans who shouldn't even be in the country in the first place? When you're a superpower, the line of separation between domestic and foreign policy hardly exists. During the Cold War, the Soviet Union was impressed by the way Ronald Reagan handled the blackmail by the air trafic controllers. He simply fired them. This signalled to your enemies abroad that you were not going to give into black mail anywhere.
What is at stake here is your credibility as a superpower. In the longer run, it could be your physical security from nuclear attacks, perhaps even your very survival as a coherent nation state.
DO NOT give in to Mexican intimidation. Build the fence, and deport the illegals. Yes, ALL of them. No amnesty.
We are facing decades of what could potentially become the deadliest war in human history, where the very survival of Western civilization and perhaps human civilization in general hangs in the balance. We cannot win this without you. You are the indispensible nation, and if you break down, the rest of the planet is basically screwed.