I was pretty young, so I don't remember how far into his second term that his struggles became apparent, but it was definitely understood to be the case by '88. His administration was pretty respected, though, even though many didn't like Nancy's level of involvement.
Electing Biden at this point would be about like electing Reagan if he were running in 1988 (or maybe 1992). His choice of a running mate is going to be more significant perhaps than any candidate in history, both from the standpoint of voter draw and for the impact on the country if his ticket wins.