Oil is strongly correlated to growth, which means with volumes of oil going down, the only direction our economy is going to take is also down: we're in for a recession and it's not going to stop soon. Now we can survive in a recession, but we (as a species) have never done it before on long durations, so it's going to be quite a challenge.
Considering that commercial fusion is nowhere near us for the next ~100 years, we're in for a very bad time.
Of course, you can in our universe for an estimated 1e38 years.
The point being that if there is a big enough supply of something that doesn't renew to last until the next breakthrough there is no problem. Never in the history of the human race has this failed.
Will oil last until we get fusion figured out? It seems to me pretty likely that's a yes.