How do you think they'd respond? With SEAL Team 6 while keeping everything quiet?
When the government shows up to force you to turn over the information, no violence is required, but you can make sure the newspapers are there when it happens, and that the knowledge of it happening is not restricted to a few execs, keeping key technical people in the dark (as happened at Yahoo)
Possibly by taking you to court and convicting you of breaking some law by refusing to provide the information the first time, perhaps even completely independently of whether or not the order was actually constitutional. I can imagine lots of bad outcomes that would land you in jail without giving you the chance to take the actual issue to court.
https://arstechnica.com/tech-policy/2016/04/in-a-reversal-ju...
Is that how it works? You can refuse anything the government tells you to do until they take you to court and the court orders you?