Thanks for joining the discord, here is what I would do:
your first move should probably be the Spin Room Session or Crisis Response to limit the immediate effect. don't try to fight back while you're already hurt. Once you've stabilized, use Rapid Response to counter-punch, since it's lower risk than full Opposition Research and built for exactly that situation. Then rebuild your favorability with a Policy Address or Coalition Building action. The biggest mistake is going straight for Opposition Research when your numbers are already down, because the backfire risk gets much worse in that state.
(Note: the current AI may not let you do those stuff even if you ask for it, will be patched tomorrow)