Console manufacturers don't run unsigned code, so I expect they'll just sit still until the next hardware refresh.
In addition they do have a store with indie games which seems to be more or less open to anyone (I assume there are some checks but I wouldn't trust them completely) much like Steam.
In other words, if I visit a site like Google or Facebook on an affected device, I can change the JavaScript that is run, and make it still appear like it came from a trusted domain.
I imagine they are more concerned about game authors snooping keys or whatnot.