A brief search suggests that most federal employees are unionized. How militant are the unions? Could they issue noncooperation guidelines to their members?
That would certainly be illegal, but anyone who still thinks we live in a time of playing by the rules is clearly not paying attention and is destined to lose.
If they want a gloves-off fight, we should give them one. If there were ever a time for unions to act fast and take militant action, it's now.