At its core, the government can enforce arbitrary declarations because they have the ability to use force against those who don't comply - ie; they control the prisons, the police and the armies.
"Political power grows out of the barrel of a gun" - Mao Zedong
At the same time, there are numerous historical examples of non-violent non-compliance nullifying that power. For example, when the Danish just refused to help the Nazis to isolate, persecute and exterminate Jews in their country, the Nazis weren't actually able to do all that much to change that.
People at Apple just refusing to assist the government is, in a way, the government's worst nightmare: it shows just how little power they actually have.
Some weak forms of political power grow out of the barrel of a gun. True power grows from the consent and support of the governed. Withdraw that consent, and the gun is shown to be a pitifully ineffective tool of government. Maybe this is a historical lesson we need to re-learn.
I dunno, it seems a bit like saying the dollar has value because of the gold in Fort Knox. Possibly it was once true, and it provides a pleasing sense of solidity to an intangible thing, but the scary reality is that it's largely down to social convention. If enough people rejected the legitimacy of government wholesale, its power would evaporate and brute force would not restore it.
Some governments may claim such a monopoly, but in the most parts of the USA, at least, private citizens have not completely delegated their right of self-defence through physical violence.
"Political power grows out of the barrel of a gun" - Mao Zedong