I'd rather face a firing squad than (do something)
I really do not want to (do something). A firing squad is a group of people assigned to execute someone by gunfire. The phrase hyperbolically implies that the speaker would rather face a gruesome death than do what is being discussed. I'd rather face a firing squad than do another presentation for the board. Last time, they found an error in my report and screamed at me for it.
I'd rather face a firing squad than do something
Fig. I would prefer to stand and be executed by gunfire than to do something. I'd rather face a firing squad than go shopping the day after Christmas.