While not fatigued, I did have to call in sick in a situation that royally screwed the operation. It was so bad that even when I called Crew Accommodations regarding transportation to the airport 30 hours later, the woman on the other end said, "Oh! Your THAT person!"
However, I never received an push back or retaliation from anyone. My initial call was forwarded to the Duty Pilot (an action that may irritate some), but the only thing the Duty Pilot wanted to know was if I needed a doctor sent to the hotel room. I didn't get defensive and treated everyone with respect. If you do get someone who you feel is pressuring you, the worst thing you can do is be a d!ck back. As long as you abide by the FARs and aren't rude, there is nothing they can do.