Let’s take a quick look back at English History and the time of Henry VIII. When push came to shove and Henry said, “sign the oath making me head of the church of England or die”. . .I believe that only Bishop (he was made cardinal just before his death) John Fisher refused to sign. The rest of the bishops of England, willy-nilly, signed the oath. And thus renounced the Catholic faith not just for them but for all the people in England. There were, and continued to be for many years into the reign of Elizabeth, as many or more Catholics in England, but they had no bishops to lead them, their services were gradually made illegal and then treasonous, etc., priests who came to serve them were martyred.
While there is no threat of death perhaps, it seems to me that there are enough bishops here (and elsewhere) whose consciences (perhaps not surprisingly like Henry’s, whose conscience ‘pricked him’ regarding his marriage to Katherine of Aragon) are ‘pricking’ them and who would defy the Pope were he to come flat out and demand that they exercise a ‘particular’ judgment even if that judgment is both historically held and doctrinally sound. And could you imagine these bishops appealing to the U.S. government to support them? Could you imagine them refusing to leave their sees if the Pope appoints another bishop? I can.