If after the 2012 election you are told:

[President Johnson]

I would have assumed that Biden was also the nominee in 2016 and Hillary didn't run, and that 2016 turned out to be some form of 2000 redux, Biden winning the popular vote while narrowly losing the Electoral College after some irregularities. The subsequent Republican president turned out to be a complete disaster and Biden, way ahead in the polls, decides to go all in for a rematch and ends up winning.

I would still have been stunned. Before 2015, I always thought Biden might run and actually win in 2016, but that he would just serve a single term since he'd be 82 at the conclusion of his second term. Heck, now we're talking about this is just his first term.

But really interesting question. I recently watched a clip of Obama around 2011 or 2012, and I asked myself how he'd react to a timetraveler telling him that Joe Biden is president ten years from there and not his immediate successor.