Where does the government get the authority to order Apple to hack one of it's customer's phones?
Why do Republican candidates who claim to support a strict interpretation of the Constitution and limited government side with the government on this issue?
Red:
The All Writs Act of 1789.
Blue:
Because folks who hold great power, or who have a reasonable expectation of soon holding it, recognize damn well that they too will want to have a means of exacting their influence in a court of law when circumstances arise for which there is no other legal guidance or precedent pertaining specifically to the situation.
The idea of the All Writs Act is consistent with the principle of representative democracy, with what it means to be a republic. In a republic, citizens choose other citizens and empower them to make the best decisions they can on the electorate's behalf. Republicans and Democrats both understand that and neither wants to see constrained their ability to do so, regardless of which party holds sway at any given moment, merely because our legal system is silent on a specific matter.