Besides Biden being the incumbent, Republicans will never ask Trump to step down, no matter what. Dems on the other hand do not think of Biden as their god-emperor and the DNC is now beginning to worry (far too late) if Biden can actually win against Trump.
Notice that many of the stories you see about this refer to the debate but not if Biden can actually win or not. The debate is not what is causing Biden to lose dem votes. Any story that says the debate is the reason for this is probably misleading at best, because I doubt they mention that Trump was lying the entire debate.