If the wet market is at fault, it can be blamed on the local party leadership, which was easy enough to do because they continued to screw up during the early stages of the pandemic. One memorable one is when they hosted a massive dinner for 20000 people in close proximity when it was starting to really heat up.
If it's the lab, that squarely falls on the national government, which in all things can and must do no wrong.
A poster above said it perfectly, when your authority comes from competency, you need to show your competent. The CCP has this precarious position in China where the people support it strongly because they've been doing a good job giving people better lives, at least from their perspective. If that turns badly in any way, it could break them.