She did one mighty job of shooting herself in the foot there. It's also funny that her current strategy of delay, delay, delay is probably just going to make everything worse for her. I think she's still going to be in power by the time everything comes to a head. She just made it later.
Being somewhat fair if the Teeth hadn't shown up at the rock she would have been replaced and gotten away with it. Of course I lost all sympathy for her when the Uppercrust meeting revealed she thinks Apeiron is highly unstable and dangerous and despite her claims of not caring about her career so she'd throw it away it a heartbeat to keep the elite out of the city she was planning on getting him a pre-signed killed order because she already had her media contacts working on smear pieces that used the fact he had one in an attempt to divert attention and blame onto him.